%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.21",
%%%     date            = "05 March 2013",
%%%     time            = "11:25:57 MST",
%%%     filename        = "stenger-frank.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "11980 5014 23457 236213",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; Green's functions;
%%%                        integral equations; multigrid sync methods;
%%%                        numerical approximation; numerical
%%%                        integration; numerical quadrature; ordinary
%%%                        differential equations; partial differential
%%%                        equations; rational approximation; Sinc
%%%                        functions",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of
%%%                        Frank Stenger, whose personal Web site
%%%                        can be found at
%%%
%%%                            http:://www.cs.utah.edu/~stenger
%%%
%%%                        The companion LaTeX file stenger-frank.ltx
%%%                        can be used to typeset this bibliography.
%%%
%%%                        At version 1.21, the year coverage looked
%%%                        like this:
%%%
%%%                             1965 (   3)    1981 (   3)    1997 (   5)
%%%                             1966 (   6)    1982 (   4)    1998 (   3)
%%%                             1967 (   1)    1983 (   2)    1999 (   4)
%%%                             1968 (   4)    1984 (  13)    2000 (   8)
%%%                             1969 (   1)    1985 (   2)    2001 (   0)
%%%                             1970 (   2)    1986 (   4)    2002 (   4)
%%%                             1971 (   5)    1987 (   4)    2003 (   0)
%%%                             1972 (   4)    1988 (   4)    2004 (   2)
%%%                             1973 (   4)    1989 (   5)    2005 (   0)
%%%                             1974 (   6)    1990 (   5)    2006 (   0)
%%%                             1975 (   7)    1991 (   2)    2007 (   2)
%%%                             1976 (   4)    1992 (   2)    2008 (   2)
%%%                             1977 (   2)    1993 (   3)    2009 (   1)
%%%                             1978 (   3)    1994 (   5)    2010 (   1)
%%%                             1979 (   4)    1995 (   7)
%%%                             1980 (   1)    1996 (   1)
%%%
%%%                             Article:         91
%%%                             Book:             3
%%%                             InCollection:     6
%%%                             InProceedings:   23
%%%                             Misc:             1
%%%                             PhdThesis:        1
%%%                             Proceedings:     21
%%%                             TechReport:       9
%%%
%%%                             Total entries:  155
%%%
%%%                        This file is available as part of the BibNet
%%%                        Project.  The master copy is available for
%%%                        public access at
%%%
%%%                            ftp://ftp.math.utah.edu in the/pub/bibnet/authors/s
%%%
%%%                        mirrored to
%%%
%%%                            ftp://netlib.bell-labs.com/netlib/bibnet/authors
%%%
%%%                        This bibliography was collected from
%%%                        multiple sources:
%%%
%%%                        * the author' own files;
%%%                        * the TeX User Group bibliography archives;
%%%                        * the very large Computer Science
%%%                          bibliography collection on ftp.ira.uka.de
%%%                          in /pub/bibliography, to which many people
%%%                          have contributed;
%%%                        * Internet library catalogs, including
%%%                          University of California MELVYL, Library of
%%%                          Congress, and OCLC;
%%%                        * the ACM Portal database;
%%%                        * the AMS MathSciNet database;
%%%                        * the Compendex database;
%%%                        * the European Mathematical Society database;
%%%                        * the IEEE Xplore database;
%%%                        * the INSPEC database;
%%%                        * the JSTOR database; and
%%%                        * the OCLC WorldCat catalog.
%%%
%%%                        BibTeX citation tags are uniformly chosen
%%%                        as name:year:abbrev, where name is the
%%%                        family name of the first author or editor,
%%%                        year is a 4-digit number, and abbrev is a
%%%                        3-letter condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        first by ascending year, and within each
%%%                        year, alphabetically by author or editor,
%%%                        and then, if necessary, by the 3-letter
%%%                        abbreviation at the end of the BibTeX
%%%                        citation tag, using the bibsort -byyear
%%%                        utility.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

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%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-nhfb =  "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org|,
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}

@String{j-ANZIAM-J              = "The ANZIAM Journal"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-MATH-NOTES       = "Applied Mathematics Notes"}

@String{j-BULL-AMS              = "Bulletin of the American Mathematical Society"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CAN-APPL-MATH-Q       = "Canadian Applied Mathematics Quarterly"}

@String{j-COMM-APPL-ANAL        = "Communications in Applied Analysis"}

@String{j-COMP-GRAPHICS         = "Computer Graphics"}

@String{j-COMPOS-SCI-TECH       = "Composites Science and Technology"}

@String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"}

@String{j-INT-J-FRACTURE        = "International Journal of Fracture"}

@String{j-INT-J-PURE-APPL-MATH  = "International Journal of Pure and Applied Mathematics"}

@String{j-J-APPROX-THEORY       = "Journal of Approximation Theory"}

@String{j-J-COMP-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-COMPLEXITY          = "Journal of Complexity"}

@String{j-J-INST-MATH-APPL      = "Journal of the Institute of Mathematics and
                                  its Applications"}

@String{j-J-INTEGRAL-EQU-APPL   = "Journal of Integral Equations and
                                  Applications"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
                                  of Standards. Section B, Mathematics and
                                  Mathematical Physics"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NUMER-ALGORITHMS      = "Numerical Algorithms"}

@String{j-NUMER-HEAT-TRANSFER-B = "Numerical Heat Transfer, Part B
                                  (Fundamentals)"}

@String{j-NUMER-METHODS-PARTIAL-DIFFER-EQU = "Numerical Methods for Partial
                                  Differential Equations"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-SPIE             = "Proceedings of the SPIE --- The International
                                  Society for Optical Engineering"}

@String{j-QUART-APPL-MATH       = "Quarterly of Applied Mathematics"}

@String{j-SIAM-J-MATH-ANA       = "SIAM Journal on Mathematical Analysis"}

@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
                                  Applied Mathematics: Series B, Numerical
                                  Analysis"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-ULTRASONIC-IMAGING    = "Ultrasonic Imaging"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-ACADEMIC-PRESS      = "Academic Press"}
@String{pub-ACADEMIC-PRESS:adr  = "New York, NY, USA"}

@String{pub-BIRKHAUSER          = "Birkh{\"{a}}user"}
@String{pub-BIRKHAUSER:adr      = "Cambridge, MA, USA; Berlin, Germany; Basel,
                                  Switzerland"}

@String{pub-BIRKHAUSER-BOSTON   = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}

@String{pub-CRC                 = "CRC Press"}
@String{pub-CRC:adr             = "2000 N.W. Corporate Blvd., Boca Raton,
                                  FL 33431-9868, USA"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-KLUWER              = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr          = "Norwell, MA, USA, and Dordrecht,
                                  The Netherlands"}

@String{pub-MARCEL-DEKKER       = "Marcel Dekker"}
@String{pub-MARCEL-DEKKER:adr   = "New York, NY, USA"}

@String{pub-NORTH-HOLLAND       = "North-Holland Publishing Co."}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PLENUM              = "Plenum Press"}
@String{pub-PLENUM:adr          = "New York, NY, USA; London, UK"}

@String{pub-SPIE                = "SPIE Optical Engineering Press"}
@String{pub-SPIE:adr            = "Bellingham, WA, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg, Germany~/
                                  London, UK~/ etc."}

@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}

%%% ====================================================================
%%% Bibliography entries, sorted by year and then by citation label,
%%% with ``bibsort -byyear'':

%%% http://www.zentralblatt-math.org/zmath/en/search/
%%% au:stenger, frank & py:1960-1965
%%% ZM has more: 1972 (1), 1976 (4), 1995 (2)

@Article{Olver:1965:EBA,
  author =       "F. W. J. Olver and F. Stenger",
  title =        "Error Bounds for Asymptotic Solutions of Second-Order
                 Differential Equations having an Irregular Singularity
                 of Arbitrary Rank",
  journal =      j-SIAM-J-NUM-ANALYSIS-B,
  volume =       "2",
  number =       "2",
  pages =        "244--249",
  month =        "????",
  year =         "1965",
  CODEN =        "????",
  ISSN =         "0887-459X (print), 1095-7170 (electronic)",
  MRclass =      "41.50 (34.00)",
  MRnumber =     "MR0185351 (32 \#2819)",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/siamjnumeranal.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/SIAMJNUMERANAL/siamjnumeranal.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0887-459X%281965%292%3A2%3C244%3AEBFASO%3E2.0.CO%3B2-N",
  acknowledgement = ack-nhfb,
}

@TechReport{Stenger:1965:EBAa,
  author =       "Frank Stenger",
  title =        "Error bounds for asymptotic solutions of differential
                 equations. 1, {The} distinct eigenvalue case",
  type =         "Technical Report",
  number =       "2",
  institution =  "Department of Computing Science, University of
                 Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "34",
  year =         "1965",
  LCCN =         "QA 76 A1 A33 no.002",
  bibdate =      "Wed May 09 10:12:54 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://web.sirsitest.library.ualberta.ca/uhtbin/cgisirsi/QWzmKzdaVV/UAARCHIVES/295120075/9?first_hit=1&last_hit=20&form_type=&VIEW%5E3.x=49&VIEW%5E1.y=10",
  acknowledgement = ack-nhfb,
}

@TechReport{Stenger:1965:EBAb,
  author =       "Frank Stenger",
  title =        "Error bounds for asymptotic solutions of differential
                 equations. 2, {The} general case",
  type =         "Technical Report",
  number =       "3",
  institution =  "Department of Computing Science, University of
                 Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "44",
  year =         "1965",
  LCCN =         "QA 76 A1 A33 no.003",
  bibdate =      "Wed May 09 10:12:54 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://web.sirsitest.library.ualberta.ca/uhtbin/cgisirsi/3DeRFr4iWs/UAARCHIVES/295120075/9?first_hit=1&last_hit=20&form_type=&VIEW%5E4.x=49&VIEW%5E1.y=10",
  acknowledgement = ack-nhfb,
}

@TechReport{McNamee:1966:CFS,
  author =       "J. McNamee and F. Stenger",
  title =        "Construction of fully symmetric numerical integration
                 formulas",
  type =         "Technical Report",
  number =       "4",
  institution =  "Department of Computing Science, University of
                 Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "32",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1966:BEG,
  author =       "F. Stenger",
  title =        "Bounds on the error of {Gauss}-type quadratures",
  journal =      j-NUM-MATH,
  volume =       "8",
  number =       "2",
  pages =        "150--160",
  month =        apr,
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1966:EBA,
  author =       "Frank Stenger",
  title =        "Error bounds for asymptotic solutions of differential
                 equations. {II}: The general case",
  journal =      j-J-RES-NATL-BUR-STAND-B,
  volume =       "70",
  number =       "??",
  pages =        "187--210",
  month =        "????",
  year =         "1966",
  CODEN =        "JNBBAU",
  ISSN =         "0022-4340",
  bibdate =      "Thu May 10 16:31:06 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65L70 (Error bounds (numerical methods for ODE))
                 65L10 (Boundary value problems for ODE (numerical
                 methods))",
  ZMnumber =     "0233.65049",
}

@Article{Stenger:1966:EBAa,
  author =       "Frank Stenger",
  title =        "Error bounds for asymptotic solutions of differential
                 equations. {I}: The distinct eigenvalue case",
  journal =      j-J-RES-NATL-BUR-STAND-B,
  volume =       "70",
  number =       "??",
  pages =        "167--186",
  month =        "????",
  year =         "1966",
  CODEN =        "JNBBAU",
  ISSN =         "0022-4340",
  bibdate =      "Thu May 10 16:31:08 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65L70 (Error bounds (numerical methods for ODE))
                 65L15 (Eigenvalue problems for ODE (numerical methods))
                 65L10 (Boundary value problems for ODE (numerical
                 methods))",
  ZMnumber =     "0233.65048",
}

@Article{Stenger:1966:EBE,
  author =       "F. Stenger",
  title =        "Error bounds for the evaluation of integrals by
                 repeated {Gauss}-type formulae",
  journal =      j-NUM-MATH,
  volume =       "9",
  number =       "3",
  pages =        "200--213",
  month =        dec,
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 20:47:18 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Stenger:1966:EBS,
  author =       "Frank Stenger",
  title =        "Error Bounds for Solutions of Differential Equations",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computing Science, University of
                 Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "148",
  year =         "1966",
  bibdate =      "Wed May 09 10:09:05 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{McNamee:1967:CFS,
  author =       "J. McNamee and F. Stenger",
  title =        "Construction of fully symmetric numerical integration
                 formulas",
  journal =      j-NUM-MATH,
  volume =       "10",
  number =       "4",
  pages =        "327--344",
  month =        nov,
  year =         "1967",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.61",
  MRnumber =     "MR0219241 (36 \#2324)",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
}

@TechReport{Dolph:1968:SPH,
  author =       "Charles L. Dolph and Frank Stenger and A.
                 Wiin-Nielsen",
  title =        "On the stability problems of the
                 {Helmholtz--Kelvin--Rayleigh} type",
  type =         "Technical Report",
  number =       "08759-3-T",
  institution =  "Department of Meteorology and Oceanography, University
                 of Michigan",
  address =      "Ann Arbor, MI, USA",
  pages =        "72",
  year =         "1968",
  bibdate =      "Thu May 10 10:12:58 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1968:KPE,
  author =       "Frank Stenger",
  title =        "{Kronecker} Product Extensions of Linear Operators",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "5",
  number =       "2",
  pages =        "422--435",
  month =        jun,
  year =         "1968",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0036-1429%28196806%295%3A2%3C422%3AKPEOLO%3E2.0.CO%3B2-7",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1968:RNI,
  author =       "Frank Stenger",
  title =        "Review: {{\em Numerical Integration}}, by {Philip J.
                 Davis and Philip Rabinowitz}",
  journal =      j-SIAM-REVIEW,
  volume =       "10",
  number =       "2",
  pages =        "239--240",
  month =        apr,
  year =         "1968",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu May 10 17:20:18 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28196804%2910%3A2%3C239%3ANI%3E2.0.CO%3B2-Y",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1968:TC,
  author =       "Frank Stenger",
  title =        "A trap in computations",
  journal =      j-SIGNUM,
  volume =       "3",
  number =       "3",
  pages =        "??--??",
  month =        jul,
  year =         "1968",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Mar 5 17:26:27 MST 2007",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "See \cite{Moler:1969:MSC}.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
}

@Article{Moler:1969:MSC,
  author =       "C. B. Moler",
  title =        "More on the sphere in the corner",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "1",
  pages =        "7--7",
  month =        jan,
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Mar 5 17:26:28 MST 2007",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/tex/bib/signum.bib",
  note =         "See \cite{Stenger:1968:TC}.",
  acknowledgement = ack-nhfb,
}

@Article{Goodrich:1970:MSQ,
  author =       "R. F. Goodrich and F. Stenger",
  title =        "Movable Singularities and Quadrature",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "283--300",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.55",
  MRnumber =     "MR0275669 (43 \#1422)",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C283%3AMSAQ%3E2.0.CO%3B2-S",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@Article{Stenger:1970:AAC,
  author =       "Frank Stenger",
  title =        "The Asymptotic Approximation of Certain Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "1",
  number =       "3",
  pages =        "392--404",
  month =        aug,
  year =         "1970",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sun Nov 28 19:22:00 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/3;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
}

@Article{G:1971:RTC,
  author =       "W. G.",
  title =        "Review: {{\em Tabulation of Certain Fully Symmetric
                 Numerical Integration Formulas of Degree 7, 9 and 11}},
                 by {Frank Stenger}",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "935--935",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu May 10 16:53:59 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "://links.jstor.org/sici?sici=0025-5718%28197110%2925%3A116%3C935%3ATOCFSN%3E2.0.CO%3B2-B",
  acknowledgement = ack-nhfb,
}

@Article{McNamee:1971:WCF,
  author =       "J. McNamee and F. Stenger and E. L. Whitney",
  title =        "{Whittaker}'s Cardinal Function in Retrospect",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "113",
  pages =        "141--154",
  month =        jan,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A30 (65R05)",
  MRnumber =     "MR0301428 (46 \#586)",
  MRreviewer =   "F. J. Schuurmann",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197101%2925%3A113%3C141%3AWCFIR%3E2.0.CO%3B2-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@Article{Stenger:1971:CPA,
  author =       "Frank Stenger",
  title =        "Constructive proofs for approximation by inner
                 functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "372--386",
  month =        dec,
  year =         "1971",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  ISSN-L =       "0021-9045",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "An inner function is a function on the unit circle $T$
                 whose values almost everywhere have modulus $1$ and are
                 the radial limits of a bounded holomorphic function on
                 the open unit disk $U$. Recently, it has been proved
                 that, given a function $f$ which is Lebesgue measurable
                 and essentially bounded on $T$ and given $\epsilon >
                 0$, there exist inner functions $\phi_1, \psi_1,
                 \phi_2, \psi_2,\ldots{}, \phi_n, \psi_n$ and constants
                 $c_1,\ldots{}, c_n$ such that $|f(e^{i\theta}) -
                 lim_{r\rightarrow 1} \sum_{k=1}^n C_k \phi_k(r
                 e^{i\theta}) / \psi_k(r e^{i\theta})| < \epsilon$ a.e.
                 on $T$. The paper gives a constructive proof of this
                 result.",
  acknowledgement = ack-nhfb,
  classmath =    "*30E10 (Approximation in the complex domain)",
  ZMnumber =     "0227.30031",
}

@Article{Stenger:1971:RIS,
  author =       "Frank Stenger",
  title =        "Review: {{\em Integrals and Sums}}, by {P. C.
                 Chakravarti}",
  journal =      j-SIAM-REVIEW,
  volume =       "13",
  number =       "4",
  pages =        "582--583",
  month =        oct,
  year =         "1971",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu May 10 16:58:16 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28197110%2913%3A4%3C582%3AIAS%3E2.0.CO%3B2-1",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1971:RTD,
  author =       "Frank Stenger",
  title =        "The reduction of two dimensional integrals into a
                 finite number of one dimensional integrals",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "6",
  number =       "??",
  pages =        "278--287",
  month =        "????",
  year =         "1971",
  CODEN =        "AEMABN",
  ISSN =         "0001-9054",
  ISSN-L =       "0001-9054",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*30E20 (Integration (one complex variable))",
  ZMnumber =     "0235.30044",
}

@Article{Lipow:1972:HSC,
  author =       "Peter R. Lipow and Frank Stenger",
  title =        "How Slowly Can Quadrature Formulas Converge?",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "917--922",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197210%2926%3A120%3C917%3AHSCQFC%3E2.0.CO%3B2-R",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  classmath =    "*65D30 (Numerical integration)",
  corpsource =   "Univ. Montreal, Que., Canada",
  keywords =     "convergence of numerical methods; convergence of
                 quadrature formulae; integration",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0261.65017",
}

@Article{Stenger:1972:ASW,
  author =       "Frank Stenger",
  title =        "The approximate solution of {Wiener--Hopf} integral
                 equations",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "37",
  number =       "3",
  pages =        "687--724",
  month =        mar,
  year =         "1972",
  CODEN =        "JMANAK",
  ISSN =         "0022-247X",
  ISSN-L =       "0022-247X",
  bibdate =      "Thu May 10 10:34:25 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper develops an explicit approximate method of
                 solving the integral equation $f(x) = \int_0^\infty
                 h_1(x-t) f(t)\,dt + g(x)$, $x > 0$, where $g(x)$,
                 $h_1(x) \in L^1(R)L^2(R)$, $f(x) = g(x) = 0$ if $x <
                 0$. The approximate solution depends upon $2$
                 parameters, $h > 0$ and $k \in (0,1)$. It is shown that
                 if this equation has a unique solution, then as
                 $h\rightarrow 0^+$ and $k\rightarrow 1^-$, the
                 approximate solution converges to the unique solution
                 whenever a unique solution $f \in L^1(R) \cap L^2(R)$
                 exists for every given $g \in L^1(R) \cap L^2(R)$,
                 provided that $h \sum_i|H(ih+(1/2)h)|^2 \rightarrow
                 \int_R |H(x)|^2\,dx$ as $h\rightarrow 0^+$, where
                 $H(x)$ is the Fourier transform of $h_1(t)$. An example
                 is given which illustrates the application of the
                 method.",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1972:RQF,
  author =       "Frank Stenger",
  title =        "Review: {{\em Quadrature Formulae}}, by {A. Ghizetti
                 and A. Ossicini}",
  journal =      j-SIAM-REVIEW,
  volume =       "14",
  number =       "4",
  pages =        "662--662",
  month =        oct,
  year =         "1972",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu May 10 17:28:01 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28197210%2914%3A4%3C662%3AQF%3E2.0.CO%3B2-J",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1972:TMO,
  author =       "Frank Stenger",
  title =        "Transform methods for obtaining asymptotic expansions
                 of definite integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "3",
  number =       "??",
  pages =        "20--30",
  month =        "????",
  year =         "1972",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "With the condition $\int R|dh(t)| < \infty$,
                 asymptotic approximations are obtained to the integral
                 $\int Rf(t)dh(\lambda t)$ over the real line $R$ as
                 $\lambda \rightarrow \infty$, (a) by approximating
                 $h(x) = \int_R e^{ixt}\,dh(t)$ in a neighbourhood of $x
                 = 0$ and (b) by using a basis $\{\psi k(t)\}^n_{k=1}$,
                 where in contrast to the usual case $\psi k(t)$ need
                 not be equal to $t^{k-1}$.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A60 (Asymptotic problems in approximation) 42A38
                 (Fourier type transforms, one variable) 41A55
                 (Approximate quadratures)",
  ZMnumber =     "0237.41007",
}

@Article{Stenger:1973:AAS,
  author =       "Frank Stenger",
  title =        "An algorithm for the approximate solution of
                 {Wiener--Hopf} integral equations",
  journal =      j-CACM,
  volume =       "16",
  number =       "11",
  pages =        "708--710",
  month =        nov,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:24:11 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Stenger73;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/cacm.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm1970.bib",
  abstract =     "An explicit approximate solution f\alpha(h) is given
                 for the equation $f(t) = \int_0^\infty k(t-\tau)f(\tau)
                 \, d\tau + g(t)$, $t > 0$, where $k, g \in L_1(-\infty,
                 \infty) \cap L_2(-\infty, \infty)$, and it is assumed
                 that the classical Wiener--Hopf technique may be
                 applied to yield a solution $f \in L_1(0,\infty) \cap
                 L_2(0, \infty)$ for every such given $g$.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290R (Integral equations); C4180 (Integral
                 equations)",
  classmath =    "*65R20 (Integral equations (numerical methods))",
  corpsource =   "Univ. Utah, Salt Lake City, UT, USA",
  keywords =     "algorithm; approximate solution; convolution; Hopf;
                 integral equations; numerical methods; Wiener",
  oldlabel =     "Stenger73",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Stenger73",
  ZMnumber =     "0269.65063",
}

@Article{Stenger:1973:ASC,
  author =       "Frank Stenger",
  title =        "The approximate solution of convolution-type integral
                 equations",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "4",
  number =       "??",
  pages =        "536--555",
  month =        "????",
  year =         "1973",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65R20 (Integral equations (numerical methods)) 45E10
                 (Integral equations of the convolution type)",
  ZMnumber =     "0258.45005; 0232.45019",
}

@Article{Stenger:1973:IFB,
  author =       "Frank Stenger",
  title =        "Integration formulae based on the trapezoidal
                 formula",
  journal =      j-J-INST-MATH-APPL,
  volume =       "12",
  number =       "1",
  pages =        "103--114",
  year =         "1973",
  CODEN =        "JMTAA8",
  DOI =          "http://dx.doi.org/10.1093/imamat/12.1.103",
  ISSN =         "0020-2932",
  MRclass =      "65D30",
  MRnumber =     "52 #2158",
  MRreviewer =   "G. Blanch",
  bibdate =      "Fri Apr 5 08:08:39 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/jinstmathappl.bib;
                 http://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  note =         "See remarks \cite{Stenger:1977:RIF,Sack:1978:CSQ}.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D30 (Numerical integration)",
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  ZMnumber =     "0262.65011",
}

@Article{Stenger:1973:RAC,
  author =       "Frank Stenger",
  title =        "Review: {{\em Approximate Calculation of Multiple
                 Integrals}}, by {A. H. Stroud}",
  journal =      j-SIAM-REVIEW,
  volume =       "15",
  number =       "1",
  pages =        "234--235",
  month =        jan,
  year =         "1973",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu May 10 17:21:25 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28197301%2915%3A1%3C234%3AACOMI%3E2.0.CO%3B2-7",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gearhart:1974:ACE,
  author =       "W. B. Gearhart and F. Stenger",
  title =        "An approximate convolution equation of a given
                 response",
  crossref =     "Kirby:1974:OCT",
  pages =        "168--196",
  year =         "1974",
  MRclass =      "93C05",
  MRnumber =     "MR0479523 (57 \#18947)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper presents a number of linear numerical
                 methods which construct exponential sum approximations
                 by determining a convolution equation which is
                 approximately satisfied by the data $f(t)$.",
  acknowledgement = ack-nhfb,
}

@Article{Rahman:1974:EPP,
  author =       "Q. I. Rahman and Frank Stenger",
  title =        "An extremal problem for polynomials with a prescribed
                 zero",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "43",
  number =       "1",
  pages =        "84--90",
  month =        mar,
  year =         "1974",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0002-9939%28197403%2943%3A1%3C84%3AAEPFPW%3E2.0.CO%3B2-2",
  acknowledgement = ack-nhfb,
  classmath =    "*30C10 (Polynomials (one complex variable)) 30C15
                 (Zeros of polynomials, etc. (one complex variable))
                 30C75 (Extremal problems for (quasi-)conformal
                 mappings, other methods)",
  ZMnumber =     "0288.30005",
}

@InProceedings{Stenger:1974:CEB,
  author =       "Frank Stenger",
  title =        "On the convergence and error of the {Bubnov--Galerkin}
                 method",
  crossref =     "Bettis:1974:POU",
  pages =        "434--450",
  year =         "1974",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65R20 (Integral equations (numerical methods)) 65N30
                 (Finite numerical methods (BVP of PDE)) 65J05 (General
                 theory of numerical methods in abstract spaces) 65L99
                 (Numerical methods for ODE) 65E05 (Numerical methods in
                 complex analysis) 65D30 (Numerical integration)",
  ZMnumber =     "0275.65033",
}

@TechReport{Stenger:1974:CTD,
  author =       "Frank Stenger",
  title =        "Computing the topological degree of a mapping in
                 {${\cal R}^n$}",
  type =         "Report",
  institution =  "National Oceanic and Atmospheric Administration",
  address =      "Washington, DC, USA",
  year =         "1974",
  bibdate =      "Thu May 10 10:10:06 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chauvette:1975:ASN,
  author =       "Jean Chauvette and Frank Stenger",
  title =        "The approximate solution of the nonlinear equation
                 {$\Delta u = u - u^3$}",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "51",
  number =       "1",
  pages =        "229--242",
  month =        jul,
  year =         "1975",
  CODEN =        "JMANAK",
  ISSN =         "0022-247X",
  ISSN-L =       "0022-247X",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65N30 (Finite numerical methods (BVP of PDE)) 35J60
                 (Nonlinear elliptic equations) 35A35 (Theoretical
                 approximation to solutions of PDE)",
  ZMnumber =     "0311.65063",
}

@Article{Rosenberg:1975:LBA,
  author =       "Ivo G. Rosenberg and Frank Stenger",
  title =        "A Lower Bound on the Angles of Triangles Constructed
                 by Bisecting the Longest Side",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "130",
  pages =        "390--395",
  month =        apr,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "Graphics/imager/imager.75.bib;
                 Graphics/siggraph/75.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197504%2929%3A130%3C390%3AALBOTA%3E2.0.CO%3B2-H",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "Univ. Montreal, Montreal, Que., Canada",
  keywords =     "differential equations; finite element analysis;
                 infinite sequence; interior angle; lower bound;
                 numerical methods; partial; side; triangles constructed
                 by bisecting the longest",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Stenger:1975:AFW,
  author =       "Frank Stenger",
  title =        "An Analytic Function which is an Approximate
                 Characteristic Function",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "12",
  number =       "2",
  pages =        "239--254",
  month =        apr,
  year =         "1975",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/siamjnumeranal.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/SIAMJNUMERANAL/siamjnumeranal.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0036-1429%28197504%2912%3A2%3C239%3AAAFWIA%3E2.0.CO%3B2-V",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1975:ATD,
  author =       "Frank Stenger",
  title =        "An algorithm for the topological degree of a mapping
                 in $n$-space",
  journal =      j-BULL-AMS,
  volume =       "81",
  number =       "1",
  pages =        "179--182",
  month =        "????",
  year =         "1975",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Wed Jun 08 11:51:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://projecteuclid.org/euclid.bams/1183536266",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1975:CBC,
  author =       "Frank Stenger",
  title =        "Connection between a {Cauchy} system representation of
                 {Kalaba} and {Fourier} transforms",
  journal =      j-APPL-MATH-COMP,
  volume =       "1",
  number =       "1",
  pages =        "83--91",
  month =        jan,
  year =         "1975",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65R20 (Integral equations (numerical methods)) 42A38
                 (Fourier type transforms, one variable)",
  ZMnumber =     "0338.65063",
}

@Article{Stenger:1975:CTD,
  author =       "Frank Stenger",
  title =        "Computing the topological degree of a mapping in
                 {${\cal R}^n$}",
  journal =      j-NUM-MATH,
  volume =       "25",
  number =       "1",
  pages =        "23--38",
  month =        mar,
  year =         "1975",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Let P be connected n-dimensional polyhedron, and let
                 $b(P) = \sum_{j=1}^m t_j[Y_1(j), \ldots{}, Y_n(j)]$ be
                 the oriented boundary of $P$ in terms of oriented $n-1$
                 simplexes $t_j[Y_1(j), \ldots{}, Y_n(j)]$, where
                 $Y_i(j)$ is a vertex of a simplex and $t_j = \pm 1$.
                 Let $F=(f_1, \ldots{}, f_n)$ be a vector of real
                 continuous functions defined on $P$, and let $ F \neq
                 \theta \equiv (0,\ldots{} ,0)$ on $b(P)$. Assume that
                 for $1 < \mu \leq n$, and $\Phi \mu =(\psi^1, \ldots{},
                 \psi^\mu)$ where $\psi^i =f^{ji}$, $j_k \not = j_l$ if
                 $k \not = l$, the sets $S(A_\mu) = \{X \in
                 b(P):\Phi_\mu(X)/|\Phi_\mu(X)| = A_\mu\} \cap H_\mu$
                 and $b(P) - S(A_\mu)$ consist of a finite number of
                 connected subsets of $b(P)$, for all vectors $A_\mu =
                 (\pm 1, 0, \ldots{}, 0)$, $(0,\pm 1,0, \ldots{}, 0),
                 \ldots{}, (0,\ldots{},0,\pm 1)$ and for all $\mu - 1$
                 dimensional simplexes $H_\mu$ on $b(P)$. It is shown
                 that if $m$ is sufficiently large, and $\max_{(j;1\leq
                 k<l\leq n)} |Yk(j)-Yl(j)|$ sufficiently small, then
                 $d(F,P,\theta)$, the topological degree of $F$ at
                 $\theta$ relative to $P$, is given by $d(F,P,\theta ) =
                 (1)/(2n n!)\sum_{j = 1}^m t_j \Delta (\sgn F(Y_1^{(j)},
                 \ldots{}, \sgn F(Y_n^{(j)})))$.",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); B0290R (Integral
                 equations); C1160 (Combinatorial mathematics); C4180
                 (Integral equations)",
  classmath =    "*55M25 (Degree, etc.)",
  corpsource =   "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
                 USA",
  keywords =     "$n$ dimensional polyhedron; continuous functions;
                 mapping; simplex; subsets; topological degree;
                 topology",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0316.55007",
}

@Article{Stenger:1975:LBA,
  author =       "F. Stenger and I. Rosenberg",
  title =        "A lower Bound on the Angles of Triangles Constructed
                 by Bisecting the Longest Side",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "130",
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Graphics/imager/1975.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Graphics/siggraph/1975.bib",
  acknowledgement = ack-nhfb,
}

@Article{Harvey:1976:TDA,
  author =       "Charles Harvey and Frank Stenger",
  title =        "A two-dimensional analogue to the method of bisections
                 for solving nonlinear equations",
  journal =      j-QUART-APPL-MATH,
  volume =       "33",
  number =       "??",
  pages =        "351--368",
  month =        "????",
  year =         "1976",
  CODEN =        "QAMAAY",
  ISSN =         "0033-569X",
  ISSN-L =       "0033-569X",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65H10 (Systems of nonlinear equations (numerical
                 methods))",
  ZMnumber =     "0365.65032",
}

@InCollection{Ikebe:1976:NSH,
  author =       "Y. Ikebe and T. Y. Li and F. Stenger",
  booktitle =    "Theory of approximation, with applications (Proc.
                 Conf., Univ. Calgary, Calgary, Alta., 1975; dedicated
                 to the memory of Eckard Schmidt)",
  title =        "The numerical solution of the {Hilbert} problem",
  publisher =    pub-ACADEMIC-PRESS,
  address =      pub-ACADEMIC-PRESS:adr,
  pages =        "338--358",
  year =         "1976",
  MRclass =      "65R05",
  MRnumber =     "MR0440972 (55 \#13840)",
  MRreviewer =   "Jacob Steinberg",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Nickel:1976:EBU,
  author =       "Karl Nickel",
  title =        "Error Bounds and Uniqueness for the Solutions of
                 Nonlinear, Strongly Coupled, Parabolic Systems of
                 Differential Equations",
  type =         "MRC Technical Summary Report",
  number =       "1596",
  institution =  "Mathematics Research Center, US Department of the
                 Army",
  address =      "Madison, WI, USA",
  pages =        "20",
  year =         "1976",
  bibdate =      "Wed May 09 10:22:08 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  xxauthor =     "Frank Stenger",
  xxnote =       "Check: conflicting library catalog data??",
}

@Article{Stenger:1976:AWC,
  author =       "Frank Stenger",
  title =        "Approximations via {Whittaker}'s cardinal function",
  journal =      j-J-APPROX-THEORY,
  volume =       "17",
  number =       "3",
  pages =        "222--240",
  month =        jul,
  year =         "1976",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  ISSN-L =       "0021-9045",
  MRclass =      "41A30",
  MRnumber =     "MR0481786 (58 \#1885)",
  MRreviewer =   "R. S. Dahiya",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Whittaker's cardinal function is used to derive
                 various types of extremely accurate approximation
                 procedures, along with error bounds, for interpolating,
                 integrating, and evaluating the Fourier (over
                 $(-\infty,\infty)$ only) and the Hilbert (over
                 $(-\infty,\infty)$, $(0,\infty)$, and $(-1,1)$)
                 transforms of functions.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A30 (Approximation by other special function
                 classes) 65D20 (Computation of special functions) 65D15
                 (Algorithms for functional approximation)",
  fjournal =     "Journal of Approximation Theory",
  ZMnumber =     "0332.41013",
}

@Article{Hanson:1977:DSS,
  author =       "F. Hanson and J. M. Steele and F. Stenger",
  title =        "Distinct sums over subsets",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "66",
  number =       "1",
  pages =        "179--180",
  month =        sep,
  year =         "1977",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "10L10",
  MRnumber =     "MR0447167 (56 \#5482)",
  MRreviewer =   "S. L. G. Choi",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0002-9939%28197709%2966%3A1%3C179%3ASNDSOS%3E2.0.CO%3B2-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@Article{Stenger:1977:RIF,
  author =       "Frank Stenger",
  title =        "Remarks on {``Integration formulae based on the
                 trapezoidal formula'' (J. Inst. Math. Appl. {\bf 12}
                 (1973), 103--114)}",
  journal =      j-J-INST-MATH-APPL,
  volume =       "19",
  number =       "2",
  pages =        "145--147",
  year =         "1977",
  CODEN =        "JMTAA8",
  DOI =          "http://dx.doi.org/10.1093/imamat/19.2.145",
  ISSN =         "0020-2932",
  MRclass =      "65D30",
  MRnumber =     "MR0440879 (55 \#13747)",
  MRreviewer =   "G. Blanch",
  bibdate =      "Fri Apr 5 07:41:12 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "See \cite{Stenger:1973:IFB,Sack:1978:CSQ}.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D30 (Numerical integration)",
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  ZMnumber =     "0353.65014",
}

@Article{Sack:1978:CSQ,
  author =       "R. A. Sack",
  title =        "Comments on some quadrature formulas by {F. Stenger}",
  journal =      j-J-INST-MATH-APPL,
  volume =       "21",
  number =       "??",
  pages =        "359--361",
  year =         "1978",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  bibdate =      "Fri Apr 5 07:55:06 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/jinstmathappl.bib;
                 http://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  note =         "See \cite{Stenger:1973:IFB,Stenger:1977:RIF}.",
  acknowledgement = ack-nhfb,
  ZMnumber =     "0374.65011",
}

@Article{Stenger:1978:OCM,
  author =       "Frank Stenger",
  title =        "Optimal convergence of minimum norm approximations in
                 {$H_p$}",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "4",
  pages =        "345--362",
  month =        apr,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D30 (30A78)",
  MRnumber =     "MR0483329 (58 \#3342)",
  MRreviewer =   "Hans-Jurgen Albrand",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "A0260 (Numerical approximation and analysis); B0290F
                 (Interpolation and function approximation); C4130
                 (Interpolation and function approximation)",
  classmath =    "*41A55 (Approximate quadratures) 65D32 (Quadrature
                 formulas (numerical methods)) 65D15 (Algorithms for
                 functional approximation)",
  corpsource =   "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
                 USA",
  fjournal =     "Numerische Mathematik",
  keywords =     "convergence of numerical methods; function
                 approximation; interpolation quadrature; minimum norm
                 approximation convergence; minimum norm approximations
                 in $H_p$; optimal convergence",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0437.41030",
}

@Article{Stenger:1978:ULE,
  author =       "Frank Stenger",
  title =        "Upper and lower estimates on the rate of convergence
                 of approximations in {$H_p$}",
  journal =      j-BULL-AMS,
  volume =       "84",
  number =       "1",
  pages =        "145--148",
  year =         "1978",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  MRclass =      "65D30 (30A78)",
  MRnumber =     "MR0474714 (57 \#14348)",
  MRreviewer =   "V. Kabaila",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://projecteuclid.org/euclid.bams/1183540395",
  acknowledgement = ack-nhfb,
  classmath =    "*65D32 (Quadrature formulas (numerical methods)) 41A55
                 (Approximate quadratures)",
  ZMnumber =     "0381.65014",
}

@Article{Lundin:1979:CTA,
  author =       "L. Lundin and F. Stenger",
  title =        "Cardinal-type approximations of a function and its
                 derivatives",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "10",
  number =       "1",
  pages =        "139--160",
  month =        jan,
  year =         "1979",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "41A30 (30E10)",
  MRnumber =     "MR516759 (81c:41043)",
  MRreviewer =   "Hans-Peter Helfrich",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
}

@Article{Stenger:1979:SGM,
  author =       "Frank Stenger",
  title =        "A ``{Sinc--Galerkin}'' method of solution of boundary
                 value problems",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "85--109",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L10 (65N30)",
  MRnumber =     "MR514812 (80b:65112)",
  MRreviewer =   "Rolf Rannacher",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197901%2933%3A145%3C85%3AA%22MOSO%3E2.0.CO%3B2-S",
  abstract =     "This paper illustrates the application of a
                 `Sinc--Galerkin' method to the approximate solution of
                 linear and nonlinear second order ordinary differential
                 equations, and to the approximate solution of some
                 linear elliptic and parabolic partial differential
                 equations in the plane. The method is based on
                 approximating functions and their derivatives by use of
                 the Whittaker cardinal function. The DE is reduced to a
                 system of algebraic equations via accurate explicit
                 approximation of the inner products, the evaluation of
                 which does not require any numerical integration.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  classmath =    "*65L10 (Boundary value problems for ODE (numerical
                 methods)) 65N30 (Finite numerical methods (BVP of PDE))
                 65N35 (Collocation methods (BVP of PDE)) 33B10
                 (Elementary functions) 42A10 (Trigonometric
                 approximation)",
  corpsource =   "Dept. of Math., Univ. of British Columbia, Vancouver,
                 BC, Canada",
  fjournal =     "Mathematics of Computation",
  keywords =     "approximate solution; approximating functions;
                 approximation; boundary value problems; boundary-value
                 problems; cardinal function; Convergence Rate;
                 differential equations; function; Galerkin Procedure;
                 nonlinear; Numerical Methods; Optimal; Ordinary
                 Differential Equations; partial; Second Order Boundary
                 Value Problem; second order ordinary differential
                 equations; Sinc Galerkin method; Whittaker; Whittaker
                 Cardinal Function",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0402.65053",
}

@Article{Stenger:1979:UTT,
  author =       "Frank Stenger and Steven A. Johnson",
  title =        "Ultrasonic transmission tomography based on the
                 inversion of the {Helmholtz} wave equation for plane
                 and spherical wave insonification",
  journal =      j-APPL-MATH-NOTES,
  volume =       "4",
  number =       "3-4",
  pages =        "102--127",
  year =         "1979",
  CODEN =        "????",
  ISSN =         "0700-9224",
  MRclass =      "76Q05 (45B05 92A07)",
  MRnumber =     "MR551083 (81d:76083)",
  MRreviewer =   "V. M. Babich",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*74J10 (Bulk waves) 35J05 (Laplace equation, etc.)",
  fjournal =     "Applied Mathematics Notes",
  keywords =     "inversion of Helmholtz wave equation; planar
                 grey-scale view; ultrasonic transmission tomography",
  ZMnumber =     "0434.73024",
}

@Article{Stynes:1979:SST,
  author =       "Martin Stynes",
  title =        "A simplification of {Stenger}'s topological degree
                 formula",
  journal =      j-NUM-MATH,
  volume =       "33",
  number =       "2",
  pages =        "147--155",
  month =        jun,
  year =         "1979",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "55M25 (65H10)",
  MRnumber =     "80m:55002",
  MRreviewer =   "T. Y. Li",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "Dept. of Math., Univ. Coll., Cork, Ireland",
  keywords =     "matrix algebra; numerical methods; polyhedron;
                 topological degree formula",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Stenger:1980:AES,
  author =       "F. Stenger and M. Hagmann and J. Schwing",
  title =        "An algorithm for the electromagnetic scattering due to
                 an axially symmetric body with an impedance boundary
                 condition",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "78",
  number =       "2",
  pages =        "531--573",
  month =        dec,
  year =         "1980",
  CODEN =        "JMANAK",
  ISSN =         "0022-247X",
  ISSN-L =       "0022-247X",
  MRclass =      "78A45 (65N30)",
  MRnumber =     "MR601553 (82b:78020)",
  MRreviewer =   "D. L. Colton",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
}

@InProceedings{Stenger:1981:AUT,
  author =       "Frank Stenger",
  title =        "An algorithm for ultrasonic tomography based on
                 inversion of the {Helmholtz} equation",
  crossref =     "Allgower:1981:NSN",
  pages =        "371--406",
  year =         "1981",
  MRclass =      "92A07 (65D15 65N99)",
  MRnumber =     "MR644338 (83c:92020)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65Z05 (Applications to physics) 76K05 (Hypersonic
                 flows) 65N30 (Finite numerical methods (BVP of PDE))
                 35J05 (Laplace equation, etc.)",
  keywords =     "chapeau splines; Helmholtz equation; Rytov
                 approximation; ultrasonic tomography",
  ZMnumber =     "0461.65085",
}

@Article{Stenger:1981:NMB,
  author =       "Frank Stenger",
  title =        "Numerical methods based on {Whittaker} cardinal, or
                 sinc functions",
  journal =      j-SIAM-REVIEW,
  volume =       "23",
  number =       "2",
  pages =        "165--224",
  month =        apr,
  year =         "1981",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D30 (41-02 41A30 65-02)",
  MRnumber =     "MR618638 (83g:65027)",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Mon Jan 20 09:20:15 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28198104%2923%3A2%3C165%3ANMBOWC%3E2.0.CO%3B2-S",
  abstract =     "This paper summarizes the results known to date for
                 using sinc functions composed with other functions as
                 bases for approximations in numerical analysis.
                 Described are methods of interpolation and
                 approximation of functions and their derivatives,
                 quadrature, the approximate evaluation of transforms
                 (Hilbert, Fourier, Laplace, Hankel and Mellin) and the
                 approximate solution of differential and integral
                 equations. The methods have many advantages over
                 classical methods which use polynomials as bases. In
                 addition, all of the methods converge at an optimal
                 rate, if singularities on the boundary of approximation
                 are ignored.",
  acknowledgement = ack-nhfb,
  classmath =    "*65Dxx (Numerical approximation) 65R10 (Integral
                 transforms (numerical methods)) 41-XX (Approximation
                 theory) 44A10 (Laplace transform) 44A15 (Special
                 transforms) 42A38 (Fourier type transforms, one
                 variable) 65T40 (Trigonometric approximation and
                 interpolation) 65Lxx (Numerical methods for ODE) 65E05
                 (Numerical methods in complex analysis) 30E10
                 (Approximation in the complex domain) 30C30 (Numerical
                 methods in conformal mapping theory)",
  fjournal =     "SIAM Review. A Publication of the Society for
                 Industrial and Applied Mathematics",
  keywords =     "Fourier-transform; Hankel-transform; Hilberttransform;
                 interpolation; Laplace-transform; Mellin-transform;
                 quadrature; Whittaker cardinal function",
  ZMnumber =     "0461.65007",
}

@Article{Beighton:1982:EES,
  author =       "S. Beighton and B. Noble",
  title =        "An error estimate for {Stenger}'s quadrature formula",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "158",
  pages =        "539--545",
  month =        apr,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D30",
  MRnumber =     "83a:65021",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
}

@InCollection{Johnson:1982:WEI,
  author =       "Steven A. Johnson and Frank Stenger and Calvin Wilcox
                 and James Ball and Michael J. Berggren",
  booktitle =    "Acoustical imaging, Vol. 11 (Monterey, Calif., 1981)",
  title =        "Wave equations and inverse solutions for soft tissue",
  publisher =    "Plenum",
  address =      "New York",
  pages =        "409--424",
  year =         "1982",
  MRclass =      "92A07 (73P10)",
  MRnumber =     "MR690072 (84e:92008)",
  MRreviewer =   "G. Eason",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sikorski:1982:OQA,
  author =       "K. Sikorski",
  title =        "Optimal quadrature algorithms in {$H_p$} spaces",
  journal =      j-NUM-MATH,
  volume =       "39",
  number =       "3",
  pages =        "405--410",
  month =        oct,
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D30 (41A55)",
  MRnumber =     "84c:65045",
  MRreviewer =   "B. Boyanov",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
                 USA",
  keywords =     "approximation; approximation theory; complex plane;
                 conformal map; F. Stenger; function approximation;
                 integration; optimal error quadrature; simply connected
                 domain; unit disc",
  treatment =    "T Theoretical or Mathematical",
}

@InCollection{Stenger:1982:AUI,
  author =       "Frank Stenger",
  booktitle =    "Acoustical imaging, Vol. 11 (Monterey, Calif., 1981)",
  title =        "Asymptotic ultrasonic inversion based on using more
                 than one frequency",
  publisher =    "Plenum",
  address =      "New York",
  pages =        "425--444",
  year =         "1982",
  MRclass =      "76Q05",
  MRnumber =     "MR690073 (84h:76036)",
  MRreviewer =   "E. Pinney",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stenger:1983:ANT,
  author =       "Frank Stenger and Michael J. Berggren and Steven A.
                 Johnson and Y. Li",
  title =        "An Adaptive, Noise Tolerant, Frequency Extrapolation
                 Algorithm for Diffraction Corrected Ultrasound
                 Tomography",
  crossref =     "McAvoy:1983:IUS",
  pages =        "726--731",
  year =         "1983",
  DOI =          "http://dx.doi.org/10.1109/ULTSYM.1983.198154",
  bibdate =      "Wed May 09 18:07:17 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://ieeexplore.ieee.org/iel5/10283/32716/01535094.pdf?tp=&arnumber=1535094&isnumber=32716",
  abstract =     "A procedure was previously developed based on
                 algorithms for rational function frequency
                 extrapolation and 1-norm averaging to circumvent both
                 the effects of noise and the errors due to refracted
                 curved paths in solving the inverse scattering problem
                 in ultrasonic imaging. In this paper, the order of the
                 first two algorithms is reversed, that is the l1
                 averaging procedure is first applied and then the
                 rational function procedure is carried out,
                 extrapolating to infinite frequency. An adaptive method
                 for choosing the best rational function expansion is
                 also employed. The underlying ideas of the procedure
                 are described, and examples of reconstruction in the
                 presence and absence of Gaussian noise are illustrated.
                 These results are then compared with results of
                 previous experiments",
  acknowledgement = ack-nhfb,
}

@Article{Eiger:1984:BMS,
  author =       "A. Eiger and K. Sikorski and F. Stenger",
  title =        "A Bisection Method for Systems of Nonlinear
                 Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "367--377",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/2701.2705",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "MR792001 (86g:65102)",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/2701.2705",
  abstract =     "This paper describes an algorithm for the solution of
                 a system of nonlinear equations $F(X) = \theta$, where
                 $theta = (0, \ldots{}, 0)$ is an element of $R^n$, and
                 $F$ is a given continuous transformation of
                 $n$-dimensional simplex $S$ into $R^n (n \geq 2)$. The
                 program is based on computation of the topological
                 degree (deg) of a mapping and a simplex-bisection
                 scheme. The algorithm is primarily useful for small $n$
                 ($n \leq 5$), since the amount of work needed to
                 compute the topological degree for large $n$ is
                 significant. The size of the original simplex is
                 arbitrary, and the algorithm is globally convergent in
                 a residual sense. The algorithm is illustrated on
                 several simplified model problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
}

@InProceedings{Johnson:1984:FIA,
  author =       "S. A. Johnson and Y. Zhou and M. K. Tracy and M. J.
                 Berggren and F. Stenger",
  title =        "Fast Iterative Algorithms for Inverse Scattering
                 Solutions of the {Helmholtz} and {Riccati} Wave
                 Equations",
  crossref =     "Kaveh:1984:AI",
  pages =        "75--87",
  year =         "1984",
  bibdate =      "Wed May 09 19:00:11 2007",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Solving the inverse scattering problem for the
                 Helmholtz wave equation without employing the Born or
                 Rytov approximations is a challenging problem, but some
                 slow iterative methods have been proposed. One such
                 method suggested and demonstrated by us is based on
                 solving systems of nonlinear algebraic equations that
                 are derived by applying the method of moments to a sinc
                 basis function expansion of the fields and scattering
                 potential. In the past, we have solved these equations
                 for a 2-D object of $n \times n$ pixels in a time
                 proportional to $n^5$. We now describe further progress
                 in the development of new methods based on FFT
                 convolution and the concept of backprojection, which
                 solves these equations in time proportional to $n^3
                 \times \log n$.",
  acknowledgement = ack-nhfb,
}

@Article{Johnson:1984:ISS,
  author =       "S. A. Johnson and Y. Zhou and M. L. Tracey and M. J.
                 Berggren and F. Stenger",
  title =        "Inverse scattering solutions by a sinc basis, multiple
                 source, moment method. {Part III}: {Fast} algorithms",
  journal =      j-ULTRASONIC-IMAGING,
  volume =       "6",
  number =       "1",
  pages =        "103--116",
  month =        jan,
  year =         "1984",
  CODEN =        "ULIMD4",
  ISSN =         "0161-7346",
  ISSN-L =       "0161-7346",
  bibdate =      "Thu May 10 16:30:30 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Johnson:1984:RDS,
  author =       "S. A. Johnson and M. J. Berggren and F. Stenger and C.
                 H. Wilcox and E. Jensen",
  editor =       "????",
  booktitle =    "Proceedings of the 29th Annual Meeting of the American
                 Institute of Ultrasound in Medicine, and the 13th
                 Annual Meeting of the Society of Diagnostic Medical
                 Sonographers., Kansas City, MO, USA",
  title =        "Recent Developments in Solving the Exact Acoustic
                 Inverse Scattering Problem",
  publisher =    "American Inst of Ultrasound in Medicine",
  address =      "????",
  pages =        "126--??",
  year =         "1984",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed May 09 18:56:24 2007",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Ultrasound has been used in the pulsed echo (i.e.,
                 B-scan) mode for many decades to produce images of the
                 human body. In the single scan mode the spatial
                 resolution is presently limited by the transducer
                 aperture. In the compound scan mode the resolution is
                 degraded by lack of registration due to the
                 inhomogeneous speed of sound in the body. Increasing
                 the aperture of the transducer, or using synthetic
                 apertures can improve resolution up to the theoretical
                 limit of one-half wave length (the effective
                 wavelength) if corrections for refraction are
                 incorporated into the imaging process. We have
                 developed several new algorithms for finding tissue
                 properties with high quantitative accuracy and high
                 spatial resolution. A decription is given of these
                 fast, robust inverse scattering techniques that provide
                 distortionless, quantitative images with 1/2 wavelength
                 resolution.",
  acknowledgement = ack-nhfb,
}

@Article{Sikorski:1984:AFS,
  author =       "K. Sikorski and F. Stenger and J. Schwing",
  title =        "{Algorithm 614}: {A FORTRAN} Subroutine for Numerical
                 Integration in {$H_p$}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "152--160",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/399.449",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D32 (65-04)",
  MRnumber =     "MR791983 (87a:65054b)",
  MRreviewer =   "J. B. Butler, Jr.",
  bibdate =      "Wed Dec 4 10:59:43 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/FORTRAN/fortran2.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran2.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/toms.bib;
                 http://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 http://www.math.utah.edu/pub/tex/bib/toms.bib;
                 Theory/toms.bib",
  URL =          "http://doi.acm.org/10.1145/399.449",
  abstract =     "An algorithm is given implementing a method for
                 optimal quadrature in $H_p$ space, presented in an
                 accompanying paper. The procedure is based on the
                 computation of the trapezoidal approximation to the
                 integral, together with transformation of the interval
                 of integration.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
  reviewer =     "J. B. Butler, Jr.",
}

@Article{Sikorski:1984:FSI,
  author =       "K. Sikorski and F. Stenger and J. Schwing",
  title =        "A {Fortran} Subroutine for Integration in ${H}_p$
                 Spaces",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "140--160",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/FORTRAN/fortran2.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran2.bib;
                 Misc/acm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sikorski:1984:OQS,
  author =       "K. Sikorski and F. Stenger",
  title =        "Optimal Quadratures in {$H_p$} Spaces",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "140--151",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/399.448",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D32",
  MRnumber =     "MR791982 (87a:65054a)",
  MRreviewer =   "J. B. Butler, Jr.",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://doi.acm.org/10.1145/399.448",
  abstract =     "A description is given of a family of optimal
                 quadrature formulas for approximating the integral
                 $\int f(z)\,dz$ over $w^{-1}$, where $f$ belongs to the
                 Hardy's class $H_p(D)$, $1 < p \leq +\infty$, $D$ is an
                 open simply connected domain in the complex plane, and
                 $w$ is a conformal map of $D$ onto the unit disk $U$.
                 Four different classes of domains $D_d^i$, $0 < d \leq
                 \pi /2$, $i 1, 2, 3, 4$ are considered. If the user
                 cannot specify the parameters $p$ or $d$, a
                 heuristic-termination algorithm is proposed. The
                 results of numerical tests are included.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
  reviewer =     "J. B. Butler, Jr.",
}

@InProceedings{Stenger:1984:PSR,
  author =       "Frank Stenger",
  title =        "Polynomial, sinc and rational function methods for
                 approximating analytic functions",
  crossref =     "Graves-Morris:1984:RAI",
  pages =        "49--72",
  year =         "1984",
  MRclass =      "30E10 (41A20 65E05)",
  MRnumber =     "MR783261 (87c:30055)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/UIA.bib",
  abstract =     "This paper presents practically useful constructive
                 linear methods of approximation of analytic functions
                 by polynomials, sinc functions and rational functions.
                 Spaces of functions of the type frequently encountered
                 in applications are described for approximation by each
                 method. Within these spaces, the rate of convergence of
                 each approximation is nearly optimal.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A30 (Approximation by other special function
                 classes) 41A10 (Approximation by polynomials) 41A20
                 (Approximation by rational functions)",
  keywords =     "constructive linear methods of approximation; rate of
                 convergence",
  ZMnumber =     "0577.41012",
}

@InCollection{Stenger:1984:RFF,
  author =       "F. Stenger and M. J. Berggren and S. A. Johnson and C.
                 H. Wilcox",
  booktitle =    "Wave phenomena: modern theory and applications
                 (Toronto, 1983)",
  title =        "Rational function frequency extrapolation in
                 ultrasonic tomography",
  volume =       "97",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "19--34",
  year =         "1984",
  MRclass =      "92A07 (76Q05)",
  MRnumber =     "MR801551 (86j:92006)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  series =       "North-Holland Math. Stud.",
  abstract =     "The authors describe a procedure for solving the
                 inverse scattering problem in ultrasonic imaging.
                 Although the derivation of the method is based on the
                 Helmholtz equation model $\del^2 u + k^2(l+f)u = 0$ it
                 is applicable to any model for which the spatial sound
                 pressure $u = u(r^-,k)$ satisfies an asymptotic
                 equality of the form $0(k) = 1/ik.Logu(r^-,k)|r^-sr^-d
                 = \int pF(r^-)\,ds + O(k-\sigma)$, $k \rightarrow
                 \infty$ where $k$ is proportional to the frequency, $P$
                 denotes the ray path along which pressure wave travels
                 from the source point $r^-s$ to the detector point
                 $r^-d$ and $\sigma$ is a positive constant. The method
                 is based on predicting $\phi (\infty) = \int
                 pF(r^-)\,ds$ via a rational function procedure, using
                 several values $\phi(k_1), \phi(k_2), \ldots{}, \phi
                 (k_{2m+l})$. A perturbation method for correcting for
                 curved ray paths is also described. The algorithm can
                 also be modified to image materials with more
                 complicated frequency dependent attenuation. Examples
                 of images reconstructed from computer simulated data
                 with and without Gaussian additive noise are given. The
                 beneficial effect of a noise tolerant first norm data
                 fitting algorithm in improving image quality is
                 shown.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stenger:1984:SMA,
  author =       "Frank Stenger",
  title =        "{Sinc} methods of approximate solution of partial
                 differential equations",
  crossref =     "Miller:1984:CMA",
  pages =        "40--64",
  year =         "1984",
  MRclass =      "65M99 (65N99)",
  MRnumber =     "MR794700",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper is devoted to the approximation of
                 solutions of boundary value problems based upon some
                 particular expansion of functions involving the
                 so-called sinc function.",
  acknowledgement = ack-nhfb,
  classmath =    "*65N35 (Collocation methods (BVP of PDE)) 35G15
                 (Boundary value problems for linear higher-order PDE)",
  keywords =     "sinc function expansion; Whittaker cardinal function",
  reviewer =     "P.-L. Lions",
  ZMnumber =     "0581.65082",
}

@InProceedings{Kim:1985:ISS,
  author =       "W. W. Kim and Michael J. Berggren and Steven A.
                 Johnson and Frank Stenger and Calvin H. Wilcox",
  title =        "Inverse Scattering Solutions to the Exact {Riccati}
                 Wave Equations by Iterative {RYTOV} Approximations and
                 Internal Field Calculations",
  crossref =     "McAvoy:1985:IUS",
  pages =        "878--882",
  year =         "1985",
  DOI =          "http://dx.doi.org/10.1109/ULTSYM.1985.198638",
  bibdate =      "Wed May 09 18:02:49 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://ieeexplore.ieee.org/iel5/10285/32718/01535578.pdf?tp=&arnumber=1535578&isnumber=32718",
  abstract =     "A fixed-point iterative method has been applied to
                 solve the Riccati equation for ultrasonic waves. An
                 algorithm is developed to calculate the exact field
                 when an incident plane wave is scattered by a known
                 object, whose refractive index and/or size are so large
                 that the Born or Rytov approximations would not apply.
                 Another algorithm reconstructs the scattering
                 potentials from given scattered phases measured by sets
                 of linear detectors. Simulation results are shown for
                 circularly symmetric cylindrical objects. Limitations
                 of the fixed-point algorithm are demonstrated; a Newton
                 type iterative algorithm without these limitations is
                 suggested.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Berggren:1986:UIS,
  author =       "M. J. Berggren and S. A. Johnson and B. L. Carruth and
                 W. W. Kim and F. Stenger and P. K. Kuhn",
  title =        "Ultrasound Inverse Scattering Solutions from
                 Transmission and\slash or Reflection Data",
  crossref =     "Nalcioglu:1986:IWP",
  volume =       "671",
  pages =        "114--121",
  year =         "1986",
  bibdate =      "Wed May 09 19:10:14 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Although historically the Born or Rytov linear
                 approximations have received a great deal of attention,
                 it is now more apparent that only a full nonlinear
                 formulation of the inverse scattering problem, such as
                 those we have developed, provide the accuracy for
                 quantitative clinical ultrasound imaging. Our inverse
                 scattering solutions have been developed to reconstruct
                 quantitative images of speed of sound, density, and
                 absorption using the exact Helmholtz wave equation
                 without perturbation approximations. We have developed
                 fast algorithms which are based upon Galerkin or moment
                 discretizations and use various iterative solution
                 techniques such as back propagation and descent
                 methods. In order to reconstruct images with
                 reflection-only scanner geometries we have extended our
                 algorithms to include multiple frequency data. We have
                 demonstrated a procedure for imaging inhomogeneous
                 density distributions. We also discuss the significance
                 and potential applications of these new methods.",
  acknowledgement = ack-nhfb,
}

@Article{Schaffer:1986:MSM,
  author =       "Steve Schaffer and Frank Stenger",
  title =        "Multigrid-sinc methods",
  journal =      j-APPL-MATH-COMP,
  volume =       "19",
  number =       "1--4",
  pages =        "311--319",
  month =        jul,
  year =         "1986",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65M60",
  MRnumber =     "MR849840",
  bibdate =      "Thu Feb 27 09:47:09 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Second Copper Mountain conference on multigrid methods
                 (Copper Mountain, Colo., 1985).",
  abstract =     "A Galerkin method using Whittaker cardinal or ``sinc''
                 functions as basis functions is described for the
                 solution of boundary value problems. When the solution
                 is analytic in the interior of the domain, the error of
                 approximation using $2N+1$ points is $O(e^{-\gamma
                 N^{1/2}})$ even if derivatives of the solution are
                 singular at the boundaries. A multigrid method with
                 overall complexity $O(N \log N)$ is used to solve the
                 discrete equations. This paper contains a description
                 of the multigrid-sinc algorithm along with some
                 preliminary numerical results for two-point boundary
                 value problems.",
  acknowledgement = ack-nhfb,
  classmath =    "*65L10 (Boundary value problems for ODE (numerical
                 methods)) 65L60 (Finite numerical methods for ODE)
                 34B05 (Linear boundary value problems of ODE)",
  fjournal =     "Applied Mathematics and Computation",
  keywords =     "complexity; Galerkin method; multigrid-sinc algorithm;
                 numerical results; sinc series expansion",
  reviewer =     "S. F. McCormick",
  ZMnumber =     "0612.65046",
}

@Article{Stenger:1986:ENO,
  author =       "Frank Stenger",
  title =        "Explicit, nearly optimal, linear rational
                 approximation with preassigned poles",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "175",
  pages =        "225--252",
  month =        jul,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A20 (41A25 65D15)",
  MRnumber =     "MR842132 (87g:41034)",
  MRreviewer =   "Peter Borwein",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28198607%2947%3A175%3C225%3AENOLRA%3E2.0.CO%3B2-P",
  abstract =     "This paper gives explicit rational functions for
                 interpolating and approximating functions on the
                 intervals $[-1,+1]$, $[0,+\infty]$, and
                 $[-\infty,+\infty]$. The rational functions are linear
                 in the functions to be approximated, and they have
                 preassigned poles. The error of approximation of these
                 rationals is nearly as small as the error of best
                 rational approximation with numerator and denominator
                 polynomials of the same degrees. Regions of analyticity
                 are described, which make it possible to tell a priori
                 the accuracy which we can expect from this type of
                 rational approximation.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  classmath =    "*41A20 (Approximation by rational functions) 41A25
                 (Degree of approximation, etc.) 65D15 (Algorithms for
                 functional approximation) 41A50 (Best approximation)",
  corpsource =   "Dept. of Math., Utah Univ., Salt Lake City, UT, USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "accuracy; analytic; and zeros; approximation errors;
                 epsilon algorithm; error analysis; explicit
                 nearly-optimal linear rational approximation; explicit
                 rational functions; function approximation;
                 interpolation; low-degree; Pad\'e method; poles;
                 polynomials; preassigned poles; rational approximation;
                 regions; Thiele algorithm",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0592.41019",
}

@InProceedings{Berggren:1987:PFI,
  author =       "M. J. Berggren and S. A. Johnson and B. L. Carruth and
                 W. W. Kim and F. Stenger and P. L. Kuhn",
  editor =       "????",
  booktitle =    "Acoustical Imaging: Proceedings of the International
                 Symposium (Halifax, NS, Canada)",
  title =        "Performance of Fast Inverse Scattering Solutions for
                 the Exact {Helmholtz} Equation using Multiple
                 Frequencies and Limited Views",
  publisher =    "????",
  address =      "????",
  pages =        "193--201",
  year =         "1987",
  CODEN =        "ACIGD9",
  ISBN =         "0-306-42565-3",
  ISBN-13 =      "978-0-306-42565-3",
  ISSN =         "0270-5117",
  LCCN =         "????",
  bibdate =      "Wed May 09 18:53:54 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "We have previously reported fast algorithms for
                 imaging by acoustical inverse scattering using the
                 exact (not linearized) Helmholtz wave equation. We now
                 report numerical implementations of these algorithms
                 which allow the reconstruction of quantitative images
                 of speed of sound, density, and absorption from either
                 transmission or reflection data. We also demonstrate
                 the application of our results to larger grids (up to
                 64 multiplied by 64 pixels) and compare our results
                 with analytically derived data, which are known to be
                 highly accurate, for scattering from right circular
                 cylindrical objects. We report on the performance of
                 our algorithms for both transmission and reflection
                 data and for the simultaneous solution of scattering
                 components corresponding to speed of sound and
                 absorption. We have further examined the performance of
                 our methods with various amounts of random noise added
                 to the simulated data. We also report on the
                 performance of one technique we have devised to extract
                 quantitative density images from our algorithms.",
  acknowledgement = ack-nhfb,
}

@Misc{Kearfott:1987:SFF,
  author =       "R. B. Kearfott and K. Sikorski and F. Stenger",
  title =        "A {Sinc} Function Fast {Poisson} Solver",
  year =         "1987",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kim:1987:AIS,
  author =       "W. W. Kim and S. A. Johnson and M. J. Berggren and F.
                 Stenger and C. H. Wilcox",
  title =        "Analysis of Inverse Scattering Solutions from Single
                 Frequency, Combined Transmission and Reflection Data
                 for the {Helmholtz} and {Riccati} Exact Wave
                 Equations",
  crossref =     "Jones:1987:AIP",
  pages =        "359--369",
  year =         "1987",
  bibdate =      "Wed May 09 18:58:14 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Various numerical methods to solve the exact inverse
                 scattering problem are presented here. These methods
                 consist of the following steps: first, modeling the
                 scattering of acoustic waves by an accurate wave
                 equation; second, discretizing this equation; and
                 third, numerically solving the discretized equations.
                 The fixed-point method and the nonlinear
                 Newton--Raphson method are applied to both the
                 Helmholtz and Riccati exact wave equations after
                 discretizations by the moment method or by the discrete
                 Fourier transform methods. Validity of the proposed
                 methods is verified by computer simulation, using exact
                 scattering data from the analytical solution for
                 scattering from right circular cylindrical objects.",
  acknowledgement = ack-nhfb,
}

@Article{Ang:1988:NTP,
  author =       "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and
                 Fritz Keinert and Frank Stenger",
  title =        "A nonlinear two-phase {Stefan} problem with melting
                 point gradient: a constructive approach",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "245--255",
  month =        aug,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "35R35 (65P05)",
  MRnumber =     "MR959479 (89h:35350)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper considers a one-dimensional two-phase
                 Stefan problem, modeling a layer of solid material
                 floating on liquid. The model includes internal heat
                 sources, variable total mass (resulting e.g., from
                 sedimentation or erosion), and a pressure-dependent
                 melting point. The problem is reduced to a set of
                 nonlinear integral equations which provides the basis
                 for an existence and uniqueness proof and a new
                 numerical method. Numerical results are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
}

@Article{Bialecki:1988:SNM,
  author =       "Bernard Bialecki and Frank Stenger",
  title =        "{Sinc--Nystr{\"o}m} method for numerical solution of
                 one-dimensional {Cauchy} singular integral equation
                 given on a smooth arc in the complex plane",
  journal =      j-MATH-COMPUT,
  volume =       "51",
  number =       "183",
  pages =        "133--165",
  month =        jul,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65R20",
  MRnumber =     "MR942147 (89g:65163)",
  MRreviewer =   "M. S. Abou El-Seoud",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28198807%2951%3A183%3C133%3ASMFNSO%3E2.0.CO%3B2-7",
  abstract =     "The authors consider singular integral equations of
                 the type $aw+bSw+K_1w=f_1$, where $Sw(t):=\frac{1}{\pi
                 i}p.v.\int_{L}\frac{w(\tau)d\tau}{\tau -t}$, $K_
                 1w(t):=\int_{L}k_1(t,\rho)w(\tau)d\tau$. The integrals
                 are taken over a smooth, open arc $L$ of finite length
                 in the complex plane, the integral operator $S$ being
                 defined as a Cauchy principle value integral. $a,b,f_1$
                 and $k_1$ are complex functions, given on L. In order
                 to solve the equation numerically, the approximation
                 following Nystr{\"o}m's method, based on sinc
                 quadrature rules, is studied. Sinc quadrature rules are
                 rules developed by the second author [SIAM Rev. 23,
                 165-224 (1981; Zbl 0461.65007)] particularly for the
                 numerical integration of complex functions. After some
                 transformation, they are applied on the integral
                 equation. Error estimates for the numerical solution
                 are derived. The authors report of numerical examples,
                 but do not give exact figures.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290R (Integral equations); B0290B (Error analysis in
                 numerical methods); C4180 (Integral equations); C4110
                 (Error analysis in numerical methods)",
  classmath =    "*65R20 (Integral equations (numerical methods)) 65R20
                 (Integral equations (numerical methods)) 45E05
                 (Integral equations with kernels of Cauchy type)",
  corpsource =   "Utah Univ., Salt Lake City, UT, USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "Cauchy singular integral equation; Nystr{\"o}m's
                 method; sinc quadrature rules; Error estimates;
                 numerical examples; Cauchy; Cauchy singular integral
                 equation; complex plane; convergence rate; error; error
                 analysis; Fredholm integral equation; integral
                 equations; N-point approximation; numerical methods;
                 numerical solution; principal value integrals;
                 regularization procedure; Sinc function; Sinc
                 quadrature rule; Sinc--Nystr{\"o}m method; smooth arc",
  reviewer =     "G. H{\"a}mmerlin",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0662.65120",
}

@Article{Dikshit:1988:RTW,
  author =       "H. P. Dikshit and A. Sharma and V. Singh and F.
                 Stenger",
  title =        "{Rivlin}'s theorem on {Walsh} equiconvergence",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "3",
  pages =        "339--349",
  month =        mar,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045",
  ISSN-L =       "0021-9045",
  MRclass =      "30E10 (41A20)",
  MRnumber =     "MR934798 (89g:30071)",
  MRreviewer =   "P. Lappan",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The method of T. J. Rivlin (see ibid., vol.36, p.
                 334--345, 1982) is based on the properties of Chebyshev
                 polynomials and their zeros. This makes a further
                 extension of his results difficult. The authors propose
                 a mixed problem of interpolation and
                 $\ell_2$-approximation and extend Rivlin's result in
                 two directions. As a special case they obtain `help'
                 functions which give larger regions of
                 equiconvergence.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
}

@Article{Stenger:1988:RCC,
  author =       "Frank Stenger",
  title =        "Review: {{\em Computational Complexity}}, by {K.
                 Wagner and G. Wechsung}",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "2",
  pages =        "353--354",
  month =        jun,
  year =         "1988",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu May 10 17:18:35 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28198806%2930%3A2%3C353%3ACC%3E2.0.CO%3B2-B",
  acknowledgement = ack-nhfb,
}

@Article{Ang:1989:CVR,
  author =       "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and John
                 Lund and Frank Stenger",
  title =        "Complex variable and regularization methods of
                 inversion of the {Laplace} transform",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "188",
  pages =        "589--608",
  month =        oct,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65R10 (44A10)",
  MRnumber =     "MR983558 (90e:65180)",
  MRreviewer =   "A. J. Rodrigues",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28198910%2953%3A188%3C589%3ACVARMO%3E2.0.CO%3B2-H",
  abstract =     "The authors derive three new methods for the numerical
                 inversion of the Laplace transform, i.e., of obtaining
                 accurate approximations to a function $f\in
                 L^2({\bbfR}^+)$, where ${\bbfR}^+:=(0,\infty)$,
                 satisfying the equation $(*)\quad \int^{\infty}_{0}e^{-
                 st}f(t)dt=g(s),$ where $g$ is a given function in
                 $L^2({\bbfR}^+)$. The first method is based on a
                 rational approximation of $g$ by a sinc-like function
                 $(\sin c x:=(\sin x)/x).$ The second method is based on
                 a sinc solution of the integral equation (*) via
                 standard regularization. The third method is based on
                 first converting (*) to a convolution integral equation
                 over ${\bbfR}$ (using a well known change of variables)
                 and then finding a sinc approximation to the solution
                 via the application of a special regularization
                 procedure to solve the Fourier transform problem. The
                 authors obtain bounds on the error of approximation,
                 which depend on both the method of approximation and
                 the regularization parameter. The main features and
                 scope (and limitations) of each of the three methods
                 are clearly delineated. This paper is an important
                 addition to the vast literature on the numerical
                 inversion of the Laplace transform in which proposed
                 methods are backed up by thorough analyses and tested
                 on specific functions.",
  abstract2 =    "Three methods are derived for approximating $f$, given
                 its Laplace transform $g$ on $(0, \infty)$, i.e.,
                 $\int_0^\infty f(t) exp(-st)\,dt = g(s)$. Assuming that
                 $g \in L^2(0, \infty)$, the first method is based on a
                 Sinc-like rational approximation of $g$, the second on
                 a Sinc solution of the integral equation $\int_0^\infty
                 f(t) \exp (-st)\, dt = g(s)$ via standard
                 regularization, and the third method is based on first
                 converting $\int_0^\infty f(t) \exp (-st)\, dt = g(s)$
                 to a convolution integral over $R$, and then finding a
                 Sinc approximation to $f$ via the application of a
                 special regularization procedure to solve the Fourier
                 transform problem. The paper also obtains bounds on the
                 error of approximation, which depends on both the
                 method of approximation and the regularization
                 parameter.",
  acknowledgement = ack-nhfb,
  classcodes =   "C1130 (Integral transforms); C4130 (Interpolation and
                 function approximation); C4180 (Integral equations)",
  classmath =    "*65R10 (Integral transforms (numerical methods)) 65R20
                 (Integral equations (numerical methods)) 65R20
                 (Integral equations (numerical methods)) 44A10 (Laplace
                 transform) 45E10 (Integral equations of the convolution
                 type)",
  corpsource =   "Dept. of Math., Ho Chi Minh City Univ., Viet Nam",
  fjournal =     "Mathematics of Computation",
  keywords =     "approximation theory; bounds; complex variable
                 methods; convolution integral; convolution integral
                 equation; equations; error of approximation; Fourier
                 transform; Fourier transforms; integral; integral
                 equation; Laplace; Laplace transform; Laplace
                 transforms; numerical inversion; problem; rational
                 approximation; regularization; regularization methods;
                 sinc approximation; Sinc solution; sinc-like function;
                 Sinc-like rational approximation; transform",
  reviewer =     "M. Z. Nashed",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0676.65136",
}

@Article{Ang:1989:VFD,
  author =       "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and Tim
                 Folias and Fritz Keinert and Frank Stenger",
  title =        "Viscoplastic flow due to penetration: a free boundary
                 value problem",
  journal =      j-INT-J-FRACTURE,
  volume =       "39",
  number =       "1-3",
  pages =        "121--127",
  year =         "1989",
  CODEN =        "IJFRAP",
  ISSN =         "0376-9429",
  ISSN-L =       "0376-9429",
  MRclass =      "35R35 (35K20 45G05 73F15)",
  MRnumber =     "MR989695 (90c:35203)",
  MRreviewer =   "Shuzi Zhou",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Fracture",
}

@Article{Kowalski:1989:OCR,
  author =       "Marek A. Kowalski and Frank Stenger",
  title =        "Optimal complexity recovery of band- and
                 energy-limited signals. {II}",
  journal =      j-J-COMPLEXITY,
  volume =       "5",
  number =       "1",
  pages =        "45--59",
  month =        mar,
  year =         "1989",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  MRclass =      "41A05 (41A65 94A12)",
  MRnumber =     "MR990811 (90c:41003)",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper deals with the recovery of band- and
                 energy-limited signals in $L_p(I)$-norm from Hermitian
                 information gathered on a given finite interval I. Let
                 $m_p(\epsilon)$ be the minimal number of the
                 information pieces required to find an
                 $\epsilon$-accurate approximation to any such signal.
                 We shall prove that $$ \lim_{\epsilon \to
                 0^+}\frac{m_o(\epsilon)\log \log (1/\epsilon)}{\log
                 (1/\epsilon)}=1 $$ for any $p$ in $[1,\infty]$, and
                 that for sufficiently small $\epsilon &gt;0$, Hermitian
                 interpolation using $m_ p(\epsilon)(1+o(1))$ arbitrary
                 nodes yields an $\epsilon$-approximation in
                 $L_p(I)$-norm with almost minimal cost. [For part I see
                 ibid. 2, 239-254 (1986; Zbl 0626.94005).]",
  acknowledgement = ack-nhfb,
  classmath =    "*94A12 (Signal theory)",
  fjournal =     "Journal of Complexity",
  keywords =     "Hermitian information; Hermitian interpolation;
                 recovery of band- and energy-limited signals",
  ZMnumber =     "0672.94001",
}

@InProceedings{Stenger:1989:EAM,
  author =       "Frank Stenger",
  title =        "Explicit approximate methods for computational control
                 theory",
  crossref =     "Bowers:1989:CCP",
  pages =        "299--316",
  year =         "1989",
  MRclass =      "93B40",
  MRnumber =     "MR1046859",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The author considers a number of approximations for
                 functions which are suitable for use over an infinite
                 interval. It is stated that these approximations will
                 be useful for evaluating Laplace transforms, and their
                 inverses, and may also be used to approximate to
                 filter, step and delta functions.",
  acknowledgement = ack-nhfb,
  classmath =    "*93B40 (Computational methods in systems theory) 65D30
                 (Numerical integration) 65R10 (Integral transforms
                 (numerical methods))",
  keywords =     "Laplace transforms, and their inverses",
  reviewer =     "L. G. Chambers",
  ZMnumber =     "0704.93021",
}

@InProceedings{Ikebe:1990:RAS,
  author =       "Yasuhiko Ikebe and Marek Kowalski and Frank Stenger",
  title =        "Rational approximation of the step, filter, and
                 impulse functions",
  crossref =     "Wong:1990:ACA",
  pages =        "441--454",
  year =         "1990",
  MRclass =      "41A20 (30E10)",
  MRnumber =     "MR1052446 (91c:41041)",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The authors give rational approximants $H_N(\omega)$
                 (where $N$ is the cut-off index for a doubly infinite
                 series) to the Heaviside function $H(\omega)$, to the
                 filter function $\chi(\omega)$ (which is nothing else
                 but the characteristic function for the interval
                 $(-1,1)$, with value $1/2$ at $\pm 1$) using $H_
                 N((1+\omega)/(1-\omega))$ and to the Dirac delta
                 function using $H_N'(\omega)$. The results include
                 estimates for the error in the approximation as a
                 function of the parameter $N$. For the Delta function
                 the result is of the following form: $$
                 \int^{\infty}_{-\infty}H_ N(\omega)f(\omega)d\omega
                 =f(0)+O(\omega (f;\exp (-(\pi
                 /2)(N+1)^{1/2}))+O(N^{-1/2})),\quad N\to \infty, $$ for
                 $f$ continuous and bounded on the real axis and
                 absolutely integrable over $(-\infty,\infty)$ and where
                 $\omega(f;.)$ is the ordinary modulus of continuity.
                 The proofs are straightforward and lucid.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A20 (Approximation by rational functions)",
  keywords =     "Delta function; filter function",
  reviewer =     "M. G. de Bruin",
  ZMnumber =     "0701.41023",
}

@Article{Stenger:1990:RRA,
  author =       "Frank Stenger",
  title =        "Review: {{\em Rational Approximation of Real
                 Functions}} by {P. P. Petrushev and V. I. Popov}",
  journal =      j-SIAM-REVIEW,
  volume =       "32",
  number =       "1",
  pages =        "187--188",
  month =        mar,
  year =         "1990",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Mon Jan 20 09:29:37 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/siamreview.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28199003%2932%3A1%3C187%3ARAORF%3E2.0.CO%3B2-R",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stenger:1990:SOR,
  author =       "Frank Stenger",
  title =        "Some open research problems in sonic and
                 electromagnetic inversion",
  crossref =     "Martin:1990:VSL",
  pages =        "73--89",
  year =         "1990",
  MRclass =      "65P05 (35R30)",
  MRnumber =     "MR1064331",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*35R30 (Inverse problems for PDE) 78A99 (Miscellaneous
                 topics in optics and electromagnetic theory)",
  ZMnumber =     "0758.35089",
}

@InProceedings{Gustafson:1991:CAA,
  author =       "Sven-{\AA}ke Gustafson and Frank Stenger",
  title =        "Convergence acceleration applied to {Sinc}
                 approximation with application to approximation of
                 $|x|^\alpha$",
  crossref =     "Bowers:1991:CCI",
  pages =        "161--171",
  year =         "1991",
  MRclass =      "41A30 (93B40)",
  MRnumber =     "MR1140021",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The author studies mainly the role of Chebyshev
                 acceleration of Sinc approximation. Then he considers
                 various methods of approximating $\vert x\vert^ \alpha$
                 and applies Chebyshev acceleration to the various type
                 of approximants for the case of $\alpha=1$.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A65 (Abstract approximation theory)",
  keywords =     "Chebyshev acceleration",
  reviewer =     "Zhang Ganglu (Dongying)",
  ZMnumber =     "0746.41034",
}

@InProceedings{Stenger:1992:SII,
  author =       "Frank Stenger and Brian Keyes and Mike O'Reilly and
                 Ken Parker",
  title =        "{Sinc} indefinite integration and initial value
                 problems",
  crossref =     "Genz:1992:NIR",
  pages =        "281--282",
  year =         "1992",
  MRclass =      "65D30",
  MRnumber =     "MR1198912",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The sinc indefinite integral has been discussed by
                 several authors: by {\it R. B. Kearfott} [Math. Comput.
                 41, 559-572 (1983; Zbl 0523.65018)], {\it S. Haber}
                 [Two formulas for numerical indefinite integration;
                 ibid. (to appear)], and the first author [SIAM Rev. 23,
                 165-224 (1981; Zbl 0461.65007)]. The following
                 presentation summarizes some of the results in the
                 monograph by the first author [Sinc numerical methods.
                 Textbook (to appear)], involving both sinc indefinite
                 integration and the application of this formula to the
                 solution of initial value problems in ordinary
                 differential equations.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D30 (Numerical integration) 65L05 (Initial value
                 problems for ODE (numerical methods)) 34A34 (Nonlinear
                 ODE and systems, general) 41A55 (Approximate
                 quadratures)",
  keywords =     "initial value problems; sinc indefinite integration",
  ZMnumber =     "0742.65015",
}

@Book{Stenger:1993:NMB,
  author =       "Frank Stenger",
  title =        "Numerical methods based on {Sinc} and analytic
                 functions",
  volume =       "20",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 565",
  year =         "1993",
  ISBN =         "0-387-94008-1 (New York), 3-540-94008-1 (Berlin)",
  ISBN-13 =      "978-0-387-94008-3 (New York), 978-3-540-94008-1
                 (Berlin)",
  LCCN =         "QA372 .S82 1993",
  MRclass =      "65-01 (41A05 41A55 65-02)",
  MRnumber =     "MR1226236 (94k:65003)",
  MRreviewer =   "B. Boyanov",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/numana.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/numana.bib;
                 http://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "Springer Series in Computational Mathematics",
  abstract =     "This excellent monograph offers a self-contained
                 presentation of the sinc method and its application to
                 the numerical solution of integral and differential
                 equations. This book will be the standard reference for
                 the sinc method. It is of interest for mathematicians,
                 computational scientists and graduate students.\par

                 Let $h&gt;0$ and $\text {sinc} (x) : = (\pi x)^{-1}
                 \sin (\pi x)$. Using the basis functions $$S(k,h) (x) :
                 = \text {sinc} \bigl( (x - kh)/h \bigr),$$ a given
                 function $f$ bounded on the real line is approximated
                 by the cardinal function $$C(f,h) (x) : = \sum^
                 {\infty_{k = -\infty} f(kh) S(k,h) (x)}.$$ First, the
                 approximation of $f$ by means of $C(f,h)$ was studied
                 by de la Vall\'ee Poussin and Whittaker. Later,
                 Shannon's sampling theorem gave an essential impulse to
                 application of this theory in signal processing. The
                 author has special merits in this topic, since he has
                 studied the sinc method over 30 years intensively.
                 Thus, many results presented in this book are new. Note
                 that the sinc method is closely related to the
                 approximation by translates, wavelet theory, and
                 multiscale technique.\par

                 Basic facts on analytic functions, polynomial
                 approximation, and Fourier technique are presented in
                 the first two chapters. Chapter 3 deals with the
                 approximation of $f$ by $C(f,h)$, where $f$ is analytic
                 on a strip containing the real line. Interpolation,
                 quadrature, Fourier and Hilbert transforms,
                 derivatives, and indefinite integrals are determined
                 approximately. All of these procedures converge at
                 exponential and close to optimal rate. Using a
                 conformal mapping, the results of Chapter 3 are
                 extended in Chapter 4 to approximations over a contour
                 such that a finite or semi-infinite interval is a
                 special case.\par

                 In Chapter 5, procedures related to sinc methods are
                 discussed. Chapter 6 illustrates the application of
                 sinc methods to the approximate solution of integral
                 equations. The author considers nonlinear Volterra
                 integral equations, Cauchy singular integral equations,
                 convolution equations, Wiener--Hopf integral equations,
                 and the inversion of Laplace transform. If there exists
                 an analytic solution, then it is shown that an
                 exponential convergence rate is reachable by sinc
                 methods.\par

                 Finally, Chapter 7 demonstrates the use of sinc methods
                 to obtain approximate solutions of ordinary and partial
                 differential equations for both initial and boundary
                 value problems. It is pointed out that Galerkin, finite
                 element, spectral, and collocation methods are
                 essential the same for the sinc methods, since they all
                 yield nearly the same system of linear equations, whose
                 solutions have the same order of accuracy.\par

                 Each section ends with some problems. Each chapter
                 closes with historical remarks. This book is completed
                 by a detailed list of references containing 296
                 items.",
  acknowledgement = ack-nhfb,
  classmath =    "*65T40 (Trigonometric approximation and interpolation)
                 65-02 (Research monographs (numerical analysis)) 42C05
                 (General theory of orthogonal functions and
                 polynomials) 65N30 (Finite numerical methods (BVP of
                 PDE)) 65N35 (Collocation methods (BVP of PDE)) 65L60
                 (Finite numerical methods for ODE) 65M70 (Spectral,
                 collocation and related methods (IVP of PDE)) 65R20
                 (Integral equations (numerical methods)) 42A38 (Fourier
                 type transforms, one variable) 94A12 (Signal theory)
                 65Dxx (Numerical approximation) 44A10 (Laplace
                 transform) 45Exx (Singular integral equations) 45G10
                 (Nonsingular nonlinear integral equations)",
  keywords =     "cardinal function; Cauchy singular integral equations;
                 collocation method; convolution equations; derivatives;
                 differential equations; exponential convergence rate;
                 finite element method; Fourier and Hilbert transforms;
                 Galerkin method; Galerkin methods; indefinite
                 integrals; interpolation; inversion of Laplace
                 transform; monograph; multiscale technique; nonlinear
                 Volterra integral equations; numerical solutions;
                 quadrature; Shannon's sampling theorem; signal
                 processing; sinc method; spectral method; translates;
                 wavelet theory; Wiener--Hopf integral equations",
  reviewer =     "M. Tasche (Rostock)",
  subject =      "Galerkin methods; Differential equations; Numerical
                 solutions",
  ZMnumber =     "0803.65141",
}

@Article{Stenger:1993:RSM,
  author =       "Frank Stenger",
  title =        "Review: {{\em Sinc Methods for Quadrature and
                 Differential Equations}}, by {J. Lund and K. L.
                 Bowers}",
  journal =      j-SIAM-REVIEW,
  volume =       "35",
  number =       "4",
  pages =        "682--683",
  month =        dec,
  year =         "1993",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Mon Jan 20 09:29:37 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "URL:
                 http://links.jstor.org/sici?sici=0036-1445%28199312%2935%3A4%3C682%3ASMFQAD%3E2.0.CO%3B2-F",
  acknowledgement = ack-nhfb,
}

@InCollection{Stenger:1993:SCA,
  author =       "F. Stenger and B. Barkey and R. Vakili",
  booktitle =    "Computation and control, III (Bozeman, MT, 1992)",
  title =        "{Sinc} convolution approximate solution of {Burgers}'
                 equation",
  volume =       "15",
  publisher =    pub-BIRKHAUSER-BOSTON,
  address =      pub-BIRKHAUSER-BOSTON:adr,
  pages =        "341--354",
  year =         "1993",
  MRclass =      "65N06",
  MRnumber =     "MR1247487",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  series =       "Progr. Systems Control Theory",
  acknowledgement = ack-nhfb,
}

@Article{Chan:1994:NPB,
  author =       "Kwong-Yu Chan and Douglas Henderson and Frank
                 Stenger",
  title =        "Nonlinear {Poisson--Boltzmann} equation in a model of
                 a scanning tunneling microscope",
  journal =      j-NUMER-METHODS-PARTIAL-DIFFER-EQU,
  volume =       "10",
  number =       "6",
  pages =        "689--702",
  year =         "1994",
  CODEN =        "NMPDEB",
  ISSN =         "0749-159X",
  ISSN-L =       "0749-159X",
  MRclass =      "65N06",
  MRnumber =     "MR1298117 (95f:65193)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper presents a finite difference application to
                 model the electrolyte solution interface between the
                 tip and the substrate in a scanning tunneling
                 microscope. An essential feature of the problem is
                 nonlinearity which makes the partial differential
                 equations that describe the problem take the form of a
                 Poisson--Boltzmann equation. The problem formulation is
                 elegant in the sense that it uses mirror imaging
                 technique to describe the boundary conditions which are
                 of Dirichlet and Neumann types.\par

                 The proposed technique is supported by numerical
                 simulation of several case studies with and without a
                 centrally adsorbed molecule. Simulation results are
                 provided and supported by comparison with those
                 obtained via analytical techniques.",
  acknowledgement = ack-nhfb,
  classmath =    "*65Z05 (Applications to physics) 65N06 (Finite
                 difference methods (BVP of PDE)) 35Q60 (PDE of
                 electromagnetic theory and optics) 78A55 (Technical
                 appl. of optics and electromagnetic theory)",
  fjournal =     "Numerical Methods for Partial Differential Equations.
                 An International Journal",
  keywords =     "electrolyte solution interface; finite difference
                 method; mirror imaging technique; nonlinear
                 Poisson-Boltzman equation; numerical examples; scanning
                 tunneling microscope",
  reviewer =     "R. Chedid (Beirut)",
  ZMnumber =     "0812.65125",
}

@Article{McArthur:1994:RNM,
  author =       "K. M. McArthur",
  title =        "Review: {{\em Numerical Methods Based on {Sinc} and
                 Analytic Functions}} ({Frank Stenger})",
  journal =      j-SIAM-REVIEW,
  volume =       "36",
  number =       "4",
  pages =        "673--674",
  month =        dec,
  year =         "1994",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Tue May 13 16:55:17 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/siamreview.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib;
                 http://www.siam.org/journals/sirev/sirev364.htm",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28199412%2936%3A4%3C673%3ANMBOSA%3E2.0.CO%3B2-J",
  acknowledgement = ack-nhfb,
}

@Article{Schmeisser:1994:RNM,
  author =       "G. Schmeisser",
  title =        "Review: {{\em Numerical Methods Based on Sinc and
                 Analytic Functions}}, by {Frank Stenger}",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "208",
  pages =        "817--819",
  month =        oct,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu May 10 17:12:05 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28199410%2963%3A208%3C817%3ANMBOSA%3E2.0.CO%3B2-K",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stenger:1994:NMT,
  author =       "Frank Stenger",
  title =        "Numerical methods via transformations",
  crossref =     "Zahar:1994:ACF",
  pages =        "543--550",
  year =         "1994",
  MRclass =      "65D30",
  MRnumber =     "MR1333642 (96a:65031)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "This paper comprises a chain of numerical quadrature
                 rules with error estimate. Some are derived from others
                 by a simple transformation. The initial element is the
                 trapezoidal rule, applied to a periodic function which
                 is analytic in a strip $|\text {Im }z|&lt; \delta$ in
                 the complex plane. The transformation $z' = \text
                 {exp}iz$ leads to a rule for integration round $|z'|=
                 1$, and applying a symmetry condition, to the Fej\'er
                 rule.\par

                 An equally interesting treatment of the doubly infinite
                 trapezoidal rule is based on error bounds for the sinc
                 series approximation, and this is related to other
                 familiar rules.\par

                 While most readers or lecturers would approach many of
                 these rules differently, all can enjoy the inter-rule
                 relationships elegantly presented in this paper.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D32 (Quadrature formulas (numerical methods)) 41A55
                 (Approximate quadratures) 65E05 (Numerical methods in
                 complex analysis) 41A80 (Remainders in approximation
                 formulas)",
  keywords =     "doubly infinite trapezoidal rule; error estimate;
                 Fej\'er rule; numerical quadrature; periodic function;
                 sinc series approximation; trapezoidal rule",
  reviewer =     "J. N. Lyness (Argonne)",
  ZMnumber =     "0829.65022",
}

@Book{Kowalski:1995:STA,
  author =       "Marek A. Kowalski and Krzysztof A. Sikorski and Frank
                 Stenger",
  title =        "Selected Topics in Approximation and Computation",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 349",
  year =         "1995",
  ISBN =         "0-19-508059-9",
  ISBN-13 =      "978-0-19-508059-9",
  MRclass =      "41-02 (65Dxx 68Q25)",
  MRnumber =     "MR1418861 (97k:41001)",
  MRreviewer =   "D. Leviatan",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/complexity.information.bib",
  URL =          "http://site.ebrary.com/lib/utah/Doc?id=10087215",
  abstract =     "As is mentioned in the Preface, this book covers basic
                 results of approximation theory. It contains also new
                 developments in the theory of moments and Sinc
                 approximation, $n$-widths, $s$-numbers and relationship
                 of these to computational algorithms. The volume
                 consists of 8 chapters. The chapter headings are: (1)
                 Classical approximation; (2) Splines; (3) Sinc
                 approximation; (4) Explicit Sinc-like methods; (5)
                 Moment problems; (6) $n$-widths and $s$-numbers; (7)
                 Optimal approximation methods; (8)
                 Applications.\par

                 Chapter 1 covers basic concepts of classical
                 approximation. The theory of best approximation is
                 presented in the setting of normed spaces. The authors
                 discuss best approximation in unitary spaces, including
                 several practically important examples. Concepts of
                 approximation in the uniform norm are presented in
                 Banach space setting.\par

                 Chapter 2 provides an introduction to basic classes of
                 polynomial splines and $B$-splines, which have
                 variation-diminishing properties when used to
                 approximate data. It is underlined that splines provide
                 useful methods of approximation in the important areas
                 of computer-aided geometric design and for representing
                 computer graphics displays.\par

                 In chapter 3 the authors present the Sinc methods as a
                 new family of self-contained methods of approximation,
                 which have several advantages over classical methods of
                 approximation in the case of the presence of end-point
                 singularities, when we have a semi-infinite or infinite
                 interval of approximation, or in the case of the
                 presence of a boundary layer situation. They introduce
                 methods of approximation and inversion of Laplace and
                 Hilbert transforms.\par

                 In chapter 4 is presented a family of simple rational
                 functions, which make possible the explicit and
                 arbitrarily accurate rational approximation of the
                 filter, the step and impulse functions.\par

                 In Chapter 5 the moment problems are discussed in the
                 setting of approximation theory, including discrete and
                 continuous moment problems of Hausdorff, Stieltjes and
                 Hamburger, as well as the discrete and continuous
                 trigonometric moment problems.\par

                 Chapter 6 deals with $n$-widths and $s$-numbers, which
                 provide conceptional generalizations of the classical
                 concepts of best approximation.\par

                 In chapter 7 are discussed optimal methods of
                 approximation and optimal algorithms for general,
                 nonlinear approximation problems. The investigation is
                 made in the general setting of normed
                 spaces.\par

                 Chapter 8 contains applications of the approximation
                 procedures presented in the previous chapters. They
                 discuss the solution of Burger's equation, the
                 approximation of band-limited signals and a nonlinear
                 zero-finding problem. Each section of the book ends
                 with a set of exercises, annotations, specific comments
                 and references. This important book can be of great
                 interest to graduate students and researchers in
                 approximation, constructive function theory and
                 numerical methods.",
  acknowledgement = ack-nhfb,
  classmath =    "*41-02 (Research monographs (approximations and
                 expansions)) 41A10 (Approximation by polynomials) 41A15
                 (Spline approximation) 65D15 (Algorithms for functional
                 approximation) 65D17 (Computer aided design (modeling
                 of curves and surfaces)) 65Y20 (Complexity and
                 performance of numerical algorithms)",
  keywords =     "moment problems; optimal approximation; splines",
  remark =       "In the fall of 1996, the authors were awarded ``First
                 Prize of the Secretary of National Education in
                 Poland'', for the research leading to the publication
                 of this monograph. This is the most prestigious
                 research award in Poland, and is awarded annually to
                 only selected groups of researchers.",
  reviewer =     "D. D. Stancu (Cluj-Napoca)",
  ZMnumber =     "0839.41001",
}

@InCollection{Morlet:1995:SAS,
  author =       "Anne C. Morlet and Frank Stenger",
  booktitle =    "Computation and control, IV (Bozeman, MT, 1994)",
  title =        "Sinc approximation of solution of heat equation with
                 discontinuous initial condition",
  volume =       "20",
  publisher =    pub-BIRKHAUSER-BOSTON,
  address =      pub-BIRKHAUSER-BOSTON:adr,
  pages =        "289--303",
  year =         "1995",
  MRclass =      "65M60",
  MRnumber =     "MR1349598",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  series =       "Progr. Systems Control Theory",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1995:CC,
  author =       "Frank Stenger",
  title =        "Collocating convolutions",
  journal =      j-MATH-COMPUT,
  volume =       "64",
  number =       "209",
  pages =        "211--235",
  month =        jan,
  year =         "1995",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D30 (41A35 65N35 65R10)",
  MRnumber =     "MR1270624 (95c:65038)",
  MRreviewer =   "Rudolf Gorenflo",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28199501%2964%3A209%3C211%3ACC%3E2.0.CO%3B2-M",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@InProceedings{Stenger:1995:SCT,
  author =       "Frank Stenger",
  title =        "{Sinc} convolution --- a tool for circumventing some
                 limitations of classical signal processing",
  crossref =     "Ismail:1995:MAW",
  pages =        "227--240",
  year =         "1995",
  MRclass =      "94A12 (44A35)",
  MRnumber =     "MR1354857 (96i:94006)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The author reviews some sinc approximation procedures
                 that are applicable to the approximate solution of
                 indefinite integral convolutions which arise in signal
                 processing problems. This sinc method works also in
                 those cases when the functions have some singularities
                 or slow decrease for large argument. Several examples
                 illustrate the limitations of classical methods via
                 fast Fourier transforms and show the advantage of sinc
                 approximation to the solution of problems in signal
                 processing.\par

                 The complete proofs can be found in Section 4.6 of the
                 author's book \cite{Stenger:1993:NMB}.",
  acknowledgement = ack-nhfb,
  classmath =    "*65T40 (Trigonometric approximation and interpolation)
                 42A10 (Trigonometric approximation) 94A12 (Signal
                 theory) 44A35 (Convolution) 42C10 (Fourier series in
                 special orthogonal functions)",
  keywords =     "fast Fourier transforms; functions with singularities;
                 functions with slow decrease; integral convolutions;
                 signal processing; sinc approximation",
  reviewer =     "M. Tasche (Rostock)",
  ZMnumber =     "0863.65093",
}

@InProceedings{Stenger:1995:SIH,
  author =       "Frank Stenger",
  title =        "{Sinc} inversion of the {Helmholtz} equation without
                 computing the forward solution",
  crossref =     "Ang:1995:IPA",
  pages =        "149--157",
  year =         "1995",
  MRclass =      "35R30 (35J05)",
  MRnumber =     "MR1327074",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Given the Helmholtz equation, $\nabla^2 u+ \kappa^2(1+
                 f) u= 0$, on a half space $H$, we sketch a procedure
                 for inversion of this equation, i.e., for
                 reconstruction of the function $f$ in $H$, via the
                 application of point sources located on the boundary of
                 $H$, without computing the solution $u$ of the forward
                 problem. Indeed, corresponding to a point $\overline r$
                 in $H$ and a point $\overline r_0$ on the exterior of
                 $H$, it is now possible to select linear combination of
                 sources such that the resulting solution $u$ measured
                 at $\overline r_0$ arbitrarily closely approximates the
                 function $f$ at $\overline r$.",
  acknowledgement = ack-nhfb,
  classmath =    "*35R30 (Inverse problems for PDE) 35J05 (Laplace
                 equation, etc.)",
  keywords =     "Helmholtz equation; plane-wave sources; point
                 sources",
  ZMnumber =     "0841.35127",
}

@Article{Stenger:1996:BRS,
  author =       "Frank Stenger",
  title =        "Book Reviews: {{\em Solving Problems in Scientific
                 Computing Using MAPLE and MATLAB}}, by {Walter Gander}
                 and {J{\'\i}r{\'\i} Hreb{\'\i}cek}",
  journal =      j-MATH-COMPUT,
  volume =       "65",
  number =       "214",
  pages =        "880--882",
  month =        apr,
  year =         "1996",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Jul 26 11:57:34 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00700-4&u=/mcom/1996-65-214/",
  acknowledgement = ack-nhfb,
}

@Article{Bojanov:1997:BRS,
  author =       "Borislav Bojanov",
  title =        "Book Review: {{\em Selected Topics in Approximation
                 and Computation}, by Marek A. Kowalski, Krzysztof A.
                 Sikorski, and Frank Stenger}",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "2",
  pages =        "333--334",
  month =        jun,
  year =         "1997",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Apr 29 18:11:34 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0036-1445%28199706%2939%3A2%3C333%3ASTIAAC%3E2.0.CO%3B2-Y",
  acknowledgement = ack-nhfb,
}

@Article{Quak:1997:BRS,
  author =       "Ewald Quak",
  title =        "Book Reviews: {{\em Selected topics in approximation
                 and computation}}, by {Marek A. Kowalski, Krzysztof A.
                 Sikorski and Frank Stenger}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "219",
  pages =        "1374--1374",
  month =        jul,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Jul 16 10:38:45 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28199707%2966%3A219%3C1374%3ASTIAAC%3E2.0.CO%3B2-L",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1997:MSM,
  author =       "Frank Stenger",
  title =        "Matrices of {Sinc} methods",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "86",
  number =       "1",
  pages =        "297--310",
  day =          "28",
  month =        nov,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65D15 (65F30)",
  MRnumber =     "MR1491441 (99b:65014)",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Special issue dedicated to William B. Gragg (Monterey,
                 CA, 1996)",
  abstract =     "The paper gives a brief review of Sinc methods, with
                 emphasis on the matrices of Sinc methods. A novel
                 procedure is presented, based on Sinc convolution, for
                 solving a Poisson problem over a rectangular region.
                 Although some of the work of Gragg (1982) may already
                 be applied to the solution of Sinc-matrix problems,
                 this paper also points to new directions of matrix
                 research.",
  acknowledgement = ack-nhfb,
  classmath =    "*65N30 (Finite numerical methods (BVP of PDE)) 35J05
                 (Laplace equation, etc.) 65T50 (Discrete and fast
                 Fourier transforms)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  keywords =     "Poisson problem; Sinc convolution; Sinc methods",
  reviewer =     "M. Z.Nashed (Newark/Delaware)",
  ZMnumber =     "0898.65066",
}

@Article{Stenger:1997:RDT,
  author =       "Frank Stenger",
  title =        "Reviews and Descriptions of Tables and Books: 22.
                 {{\em Integral equations: Theory and numerical
                 treatment}}, by {Wolfgang Hackbusch}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "220",
  pages =        "??--??",
  month =        oct,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Jul 26 11:26:13 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-220;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00843-0&u=/mcom/1997-66-220/",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1997:RIE,
  author =       "Frank Stenger",
  title =        "Review: {{\em Integral Equations: Theory and Numerical
                 Treatment}}, by {Wolfgang Hackbusch}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "220",
  pages =        "1756--1758",
  month =        oct,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu May 10 17:14:42 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28199710%2966%3A220%3C1756%3AIETANT%3E2.0.CO%3B2-V",
  acknowledgement = ack-nhfb,
}

@Article{Kress:1998:SQM,
  author =       "Rainer Kress and Ian H. Sloan and Frank Stenger",
  title =        "A sinc quadrature method for the double-layer integral
                 equation in planar domains with corners",
  journal =      j-J-INTEGRAL-EQU-APPL,
  volume =       "10",
  number =       "3",
  pages =        "291--317",
  year =         "1998",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1216/jiea/1181074232",
  ISSN =         "0897-3962",
  ISSN-L =       "0897-3962",
  MRclass =      "45L05 (45B05 65R20)",
  MRnumber =     "MR1656534 (2000b:45011)",
  MRreviewer =   "Jean M.-S. Lubuma",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://projecteuclid.org/euclid.jiea/1181074232",
  abstract =     "Let $$D_d= \{z= x+ iy; x\in R, | y|&lt;
                 d\}\subset\bbfC.$$ For $d\le \pi/2$, the function
                 $$w(z)= {1\over 1+ e^{-z}},\quad z\in\bbfC,$$ maps the
                 strip $D_d$ bijectively onto an eye-shaped domain $E_d=
                 \{w(z): z\in D_d\}$ centered around the interval
                 $(0,1)$. Let $S_{\alpha,d}$ be the space of all
                 functions $g$, which are holomorphic in $E_d$,
                 real-valued on $(0,1)$, and which satisfy $| t(1-
                 t)|^{1- \alpha}| g(t)|\le\alpha$, for $t\in E_d$. The
                 first part of the paper is devoted to sinc quadrature
                 rules for the calculation of the integral $\int^1_0
                 g(t)dt$, where $g\in S_{\alpha,d}$. A quadrature rule
                 with error $| E_{n,h}(g)|\le Ce^{-\mu n^{1/2}}\|
                 g\|_{S_{\alpha,d}}$, for some positive constants $C$
                 and $\mu$ depending on $d$ and $\alpha$ is
                 constructed.\par

                 In the second part of the paper the application of the
                 sinc quadrature method to the approximate solution of a
                 Mellin type integral equation $$\varphi(t)- \int^1_0
                 K(t,\tau)[\varphi(\tau)- \varphi(0)]d\tau+
                 \gamma(t)\varphi(0)= f(t)\tag 1$$ is investigated. The
                 kernel $K$ is assumed to have period one with respect
                 to $t$ and be continuous for $0\le t$, $\tau\le 1$ with
                 the exception of the four corners of the square
                 $[0,1]\times [0,1]$. In these corners $K$ has Mellin
                 type singularities. Let $K(t,\tau)= L(t,\tau)+
                 M(t,\tau)$, where $$| L(t,\tau)|\le {1\over \tau}
                 k\Biggl({t\over\tau}\Biggr),\quad (t,\tau)\in Q,\quad
                 t\le 1/2,$$ $$| L(t,\tau)|\le {1\over 1-\tau}
                 k\Biggl({1- t\over 1-\tau}\Biggr),\quad (t,\tau)\in
                 Q,\quad t\ge 1/2,$$ $$Q= \{(t,\tau)\in [0,1]\times
                 [0,1]: 0&lt; t+\tau&lt; 2\},$$ $$k(0)= 0,\quad
                 \int_0^\infty {k(s)\over s} ds&lt; 1.$$ For equation
                 (1) conditions of existence and uniqueness are
                 received. The quadrature method is used for an
                 approximate solution of equation (1). In this method,
                 the integral in (1) is approximated by the sinc
                 quadrature rule. Conditions of solvability of the
                 quadrature method and an error estimation are
                 obtained.\par

                 In the third part of the paper the Dirichlet problem
                 for the Laplace equation $$\Delta u= 0$$ is reduced to
                 a Mellin type integral equation.",
  acknowledgement = ack-nhfb,
  classmath =    "*65R20 (Integral equations (numerical methods)) 45E10
                 (Integral equations of the convolution type) 35J05
                 (Laplace equation, etc.) 35C15 (Integral
                 representations of solutions of PDE) 65D32 (Quadrature
                 formulas (numerical methods)) 41A55 (Approximate
                 quadratures) 65N38 (Boundary element methods (BVP of
                 PDE))",
  fjournal =     "Journal of Integral Equations and Applications",
  keywords =     "Dirichlet problem; double-layer integral equation;
                 error estimation; Laplace equation; Mellin type
                 integral equation; sinc quadrature method; sinc
                 quadrature rules",
  reviewer =     "I. V. Boikov (Penza)",
  ZMnumber =     "0916.65135",
}

@Article{Narasimhan:1998:HSS,
  author =       "S. Narasimhan and Kuan Chen and Frank Stenger",
  title =        "A harmonic-sinc solution of the {Laplace} equation for
                 problems with singularities and semi-infinite domains",
  journal =      j-NUMER-HEAT-TRANSFER-B,
  volume =       "33",
  number =       "4",
  pages =        "433--450",
  month =        jun,
  year =         "1998",
  CODEN =        "NUHTD6",
  ISSN =         "1040-7790",
  ISSN-L =       "1040-7790",
  bibdate =      "Thu May 10 10:26:37 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In this article, a recently derived harmonic sinc
                 approximation method is used to obtain approximate
                 solutions to two-dimensional steady-state heat
                 conduction problems with singularities and
                 semi-infinite domains and Dirichlet boundary
                 conditions. The first problem is conduction in a square
                 geometry, and the second one involves a semi-infinite
                 medium with a rectangular cavity. In the case of square
                 geometry, results show that the harmonic sinc
                 approximation method performs better than the
                 finite-difference and multigrid methods everywhere
                 within the computational domain, especially at points
                 close to the singularity at the upper left and right
                 corners of the square. The results from the harmonic
                 sinc approximation method for the semi-infinite domain
                 problem with a very shallow rectangular cavity agree
                 well with the analytical solution for a semi-infinite
                 domain without the cavity. The results obtained from
                 the harmonic sinc approximation also agree well with
                 the results from the finite-element package ANSYS for
                 the semi-infinite medium conduction problem with a
                 rectangular cavity of aspect ratio 1.",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1998:CSM,
  author =       "Frank Stenger and Michael J. O'Reilly",
  title =        "Computing solutions to medical problems via {Sinc}
                 convolution",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "43",
  number =       "6",
  pages =        "843--848",
  month =        jun,
  year =         "1998",
  CODEN =        "IETAA9",
  DOI =          "http://dx.doi.org/10.1109/9.679023",
  ISSN =         "0018-9286",
  ISSN-L =       "0018-9286",
  bibdate =      "Wed May 09 17:59:42 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In this paper we illustrate some novel procedures of
                 using Sinc methods to compute solutions to three types
                 of medical problems. The first of these is a novel way
                 to solve optimal control problems, the second is an
                 original way to reconstruct images for X-ray
                 tomography, and the third is a novel way to do
                 ultrasonic tomography inversion. Each of these
                 procedures uses Sinc convolution, which is a novel
                 computational procedure for obtaining accurate
                 approximations to indefinite convolutions.",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:1999:BRB,
  author =       "Frank Stenger",
  title =        "Book Reviews: {{\em Boundary element method,
                 fundamentals and applications}}, by {Frederico Paris}
                 and {Jose Canas}",
  journal =      j-MATH-COMPUT,
  volume =       "68",
  number =       "225",
  pages =        "457--459",
  month =        jan,
  year =         "1999",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (paper), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Jul 26 12:37:20 1999",
  bibsource =    "http://www.ams.org/mcom/1999-68-225;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28199901%2968%3A225%3C457%3ABEMFAA%3E2.0.CO%3B2-K;
                 http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-00992-8&u=/mcom/1999-68-225/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stenger:1999:CMS,
  author =       "Frank Stenger and Ross Schmidtlein",
  title =        "Conformal maps via {Sinc} methods",
  crossref =     "Papamichael:1999:CMF",
  pages =        "505--549",
  year =         "1999",
  MRclass =      "30C30 (41A30 65E05)",
  MRnumber =     "MR1700373 (2000i:30013)",
  MRreviewer =   "Nikos S. Stylianopoulos",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Let $B$ be a simply connected domain in the complex
                 plane with $0\in B$. The conformal mapping $f:B\to U$
                 from $B$ to the unit disc $U$ normalized by $f(0)=0$
                 can be written as $f(z)=z \exp({\cal G}(z))$ with an
                 analytic function ${\cal G}$ in $B$. This function can
                 be represented by a Cauchy integral with a real density
                 function $u$. This real function $u$ then satisfies a
                 second kind integral equation with Neumann kernel. The
                 main contribution of the paper under review consists in
                 the solution of this integral equation via Sinc
                 methods. The best reference for Sinc methods is the
                 first author's book [Numerical methods based on Sinc
                 and analytic functions (1993; Zbl 0803.65141)]. The
                 basic definitions and notions about Sinc spaces,
                 necessary for this paper, are added to the paper as an
                 appendix. The numerical algorithm is described in great
                 detail. A Fortran code may be obtained from the first
                 author. The procedure for evaluating $f$ in the
                 interior of $B$ is described as well as the
                 construction of the inverse mapping $F: U\to B$. The
                 method is applicable for regions with piecewise
                 analytic boundary curves. The convergence of the
                 numerical approximation to the solution is proven and
                 the accuracy is investigated. The complexity, i.e., the
                 work needed to achieve an approximation to $f$ with
                 error at most $\varepsilon$, is of the order
                 $O(|\log(\varepsilon)|^6)$. The complexity grows with
                 the number $n$ of analytic arcs of $\partial B$ as the
                 power $O(n^3)$. The performance of the method is
                 demonstrated at two examples, namely a semidisc and a
                 pac-man, and compared with Hough's method, which is
                 based on Symm's integral equation of the first kind.
                 The comparison ends with a draw: Each method has its
                 advantages and may be more efficient in specific
                 cases.",
  acknowledgement = ack-nhfb,
  classmath =    "*30C30 (Numerical methods in conformal mapping theory)
                 65R20 (Integral equations (numerical methods)) 41A20
                 (Approximation by rational functions)",
  keywords =     "integral equations; numerical conformal mapping; sinc
                 methods",
  reviewer =     "R. Wegmann (Garching)",
  ZMnumber =     "0948.30014",
}

@Article{Stenger:1999:OIP,
  author =       "F. Stenger and S.-{\AA}. Gustafson and B. Keyes and M.
                 O'Reilly and K. Parker",
  title =        "{ODE-IVP-PACK} via {Sinc} indefinite integration and
                 {Newton}'s method",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "20",
  number =       "2--3",
  pages =        "241--268",
  month =        jun,
  year =         "1999",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65L05 (65Y15)",
  MRnumber =     "MR1709542 (2000e:65071)",
  bibdate =      "Mon Sep 29 08:36:57 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/18/7/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/18/7/fulltext.pdf",
  abstract =     "This paper describes a package of computer programs
                 for the unified treatment of initial value problems for
                 systems of ordinary differential equations. The
                 programs implement a numerical method which is
                 efficient for a general class of differential
                 equations. The user may determine the solutions over
                 finite or infinite intervals. The solutions may have
                 singularities at the end-points of the interval for
                 which the solution is sought. Besides giving the
                 initial values and the analytical expression for the
                 differential equations to be solved the user needs to
                 specify the nature of the singularities and give some
                 other analytical information as described in the paper
                 in order to take advantage of the speed and accuracy of
                 the package described.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
}

@InProceedings{Narasimhan:2000:SIN,
  author =       "S. Narasimhan and Kuan Chen and F. Stenger",
  title =        "The solution of incompressible {Navier--Stokes}
                 equations using the sine collocation method",
  crossref =     "Kromann:2000:ISI",
  pages =        "199--214",
  year =         "2000",
  DOI =          "http://dx.doi.org/10.1109/ITHERM.2000.866827",
  bibdate =      "Wed May 09 18:10:20 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Different kind of numerical approaches have been used
                 in the past to solve the complete set of Navier--Stokes
                 equations. The traditional methods that have been used
                 in the past are the finite-difference method,
                 finite-element method and the boundary element method.
                 Multigrid methods have been used recently for solving
                 these complete set of Navier--Stokes equations and they
                 help in obtaining a faster rate of convergence of the
                 residual for the solution of these equations. Some of
                 the problems that are faced in the world of numerical
                 methods today are the capacity to handle singularities
                 that occur within or at the boundaries of a
                 computational domain and also the capacity to handle
                 semi-infinite and infinite domains. Sine numerical
                 method has the advantage of handling singularities and
                 semi-infinite domains very effectively. It also
                 provides an exponential convergence rate. This study
                 involves a first step in applying the sine numerical
                 method to the flow within a driven cavity, which
                 requires the solution of the complete two-dimensional
                 Navier--Stokes equations. The sine collocation method
                 was applied to the driven cavity problem. The
                 Navier--Stokes equations were solved by means of two
                 dimensional sine collocation using the primitive
                 variables method. Simulations were also carried out
                 with the finite-difference method for the same problem
                 and the results were matched with the sine collocation
                 method. Simulations were also carried out by using the
                 commercial CFD code FLUENT. It was seen that the
                 profiles compared well between the different methods",
  acknowledgement = ack-nhfb,
}

@Article{Resch:2000:FER,
  author =       "Ron Resch and Frank Stenger and J{\"o}rg Waldvogel",
  title =        "Functional equations related to the iteration of
                 functions",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "60",
  number =       "1-2",
  pages =        "25--37",
  year =         "2000",
  CODEN =        "AEMABN",
  ISSN =         "0001-9054",
  ISSN-L =       "0001-9054",
  MRclass =      "39B12 (26A18 30D05 37E05)",
  MRnumber =     "MR1777890 (2002j:39016)",
  MRreviewer =   "Francisco Balibrea",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Motivated by geometrical considerations the authors
                 deal with some functional equations in one variable
                 (Schr{\"o}der's equation, Babagge's equation, \dots).
                 Their special interest lies in finding situations and
                 conditions where there are unique solutions in certain
                 classes of functions. The methods and ideas presented
                 might, in the authors' opinion, be useful in
                 investigations connected with discrete dynamical
                 systems.",
  acknowledgement = ack-nhfb,
  classmath =    "*39B12 (Iterative functional equations) 30D05
                 (Functional equations in the complex domain) 26A18
                 (Iteration of functions of one real variable)",
  fjournal =     "Aequationes Mathematicae",
  keywords =     "iteration of functions; Schr{\"o}der's equation;
                 functional equations; Babagge's equation; dynamical
                 systems",
  reviewer =     "J. Schwaiger (Graz)",
  ZMnumber =     "0974.39011",
}

@Article{Stenger:2000:NSS,
  author =       "F. Stenger and R. Chaudhuri and J. Chiu",
  title =        "Novel sinc solution of the boundary integral form for
                 two-dimensional bi-material elasticity problems",
  journal =      j-COMPOS-SCI-TECH,
  volume =       "60",
  number =       "12--13",
  pages =        "2197--2211",
  month =        sep,
  year =         "2000",
  CODEN =        "CSTCEH",
  ISSN =         "0266-3538",
  ISSN-L =       "0266-3538",
  bibdate =      "Wed May 09 18:49:49 2007",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In this paper we illustrate a procedure for obtaining
                 an approximate solution of the integral equation form
                 of the two-dimensional Lame equation for a two-layer
                 problem, based on collocation via use of Sinc
                 approximation. The Sinc approach automatically
                 concentrates points near corners of the boundary where
                 the solution has singularities and yields exponential
                 convergence. A model two-layer bi-material elasticity
                 problem is numerically investigated here as an
                 illustration of this novel approach.",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:2000:SAC,
  author =       "Frank Stenger",
  title =        "{Sinc} approximation of {Cauchy}-type integrals over
                 arcs",
  journal =      j-ANZIAM-J,
  volume =       "42",
  number =       "1",
  pages =        "87--97",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "1446-1811",
  MRclass =      "30E20",
  MRnumber =     "MR1783372 (2001h:30034)",
  MRreviewer =   "D. Mitrovi{\'c}",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Papers in honour of David Elliott on the occasion of
                 his sixty-fifth birthday",
  abstract =     "The author reviews the results of {\it D. Elliott} and
                 {\it F. Strenger} [Sinc method of solution of singular
                 integral equations, in IMACS Conference on CSIE,
                 Philadelphia, PA, 155-166 (1984)] in interpolation,
                 definite integration and the approximation of Hilbert
                 transforms via the Sinc method and obtains new formulas
                 for the approximation of Cauchy-type integrals over
                 analytic arcs $$ \frac{1}{\pi i}\int
                 \frac{\varphi(\tau)}{\tau-z} d\tau $$ via the Sinc
                 method.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D32 (Quadrature formulas (numerical methods)) 41A55
                 (Approximate quadratures)",
  fjournal =     "The ANZIAM Journal. The Australian \& New Zealand
                 Industrial and Applied Mathematics Journal",
  keywords =     "Cauchy-type integrals; quadrature rules; Sinc method",
  reviewer =     "I. V. Boikov (Penza)",
  ZMnumber =     "0974.65026",
}

@Article{Stenger:2000:SSN,
  author =       "Frank Stenger",
  title =        "Summary of {Sinc} numerical methods",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "379--420",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65D15 (65-02)",
  MRnumber =     "MR1780056 (2001d:65018)",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Numerical analysis in the 20th century, Vol.\ I,
                 Approximation theory",
  abstract =     "This article attempts to summarize the existing
                 numerical methods based on Sinc approximation. Starting
                 with a comparison of polynomial and Sinc approximation,
                 basic formulas for the latter in the one-dimensional
                 case are given. The author also covers the
                 following:\par (i) Explicit spaces of analytic
                 functions for one dimensional Sinc approximation,\par
                 (ii) applications of Sinc indefinite integration and
                 collocation to the solution of ordinary differential
                 equation initial and boundary value problems,\par (iii)
                 results obtained for solution of partial differential
                 equations, via Sinc approximation of the
                 derivatives,\par (iv) some results obtained on the
                 solutions of integral equations,\par (v) use of Sinc
                 convolution, a technique for evaluating one and
                 multi-dimensional convolution-type integrals.\par A
                 list of some existing computer algorithms based on Sinc
                 methods is also given.",
  abstract2 =    "Sinc approximation methods excel for problems whose
                 solutions may have singularities, or infinite domains,
                 or boundary layers. This article summarizes results
                 obtained to date, on Sinc numerical methods of
                 computation. Sinc methods provide procedures for
                 function approximation over bounded or unbounded
                 regions, encompassing interpolation, approximation of
                 derivatives, approximate definite and indefinite
                 integration, solving initial value ordinary
                 differential equation problems, approximation and
                 inversion of Fourier and Laplace transforms,
                 approximation of Hilbert transforms, and approximation
                 of indefinite convolutions, the approximate solution of
                 partial differential equations, and the approximate
                 solution of integral equations, methods for
                 constructing conformal maps, and methods for analytic
                 continuation. Indeed, Sinc are ubiquitous for
                 approximating every operation of calculus.",
  acknowledgement = ack-nhfb,
  classmath =    "*65D15 (Algorithms for functional approximation) 65-02
                 (Research monographs (numerical analysis)) 65L60
                 (Finite numerical methods for ODE) 65M70 (Spectral,
                 collocation and related methods (IVP of PDE)) 65N35
                 (Collocation methods (BVP of PDE)) 65R20 (Integral
                 equations (numerical methods)) 65T40 (Trigonometric
                 approximation and interpolation)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  keywords =     "algorithms; analytic functions; collocation;
                 convolution-type integrals; integral equations; Sinc
                 indefinite integration; Sinc methods; survey article",
  reviewer =     "H. P. Dikshit (Bhopal)",
  ZMnumber =     "0964.65010",
}

@TechReport{Stenger:2000:TDH,
  author =       "Frank Stenger",
  title =        "Three Dimensional Hybrid {BEM--Sinc} Analysis of
                 Bonded\slash Bolted Composite Joints with Discrete
                 Cracks",
  type =         "Technical Report",
  number =       "AD-a376 152, SIN-0005",
  institution =  "Sinc. Inc.",
  address =      "Salt Lake City, UT, USA",
  pages =        "53",
  year =         "2000",
  bibdate =      "Wed May 09 10:36:19 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In this report we first illustrate a procedure for
                 obtaining an approximate solution of the boundary
                 integral equation form to the two-dimensional Lame'
                 equation for a two-layer problem, based on collocation
                 via use of Sinc approximation. The Sinc approach
                 automatically concentrates points near corners of the
                 boundary where the solution has singularities and
                 yields exponential convergence. A model two-layer
                 bi-material elasticity problem is numerically
                 investigated here as an illustration of this novel
                 approach. This is followed by altering our method of
                 solving the two dimensional problem to a ``triangular
                 form'' which has resulted in decoupling of the boundary
                 integral equation system into a sequence of subsystem
                 equations, one over each layer. Additionally, a new
                 method is derived for accurately approximating the
                 ``Laplace transform'' of the convolution kernel for the
                 case of extension of the above two dimensional solution
                 method to its three dimensional counterpart. It may be
                 noted that non-uniqueness of solution is a frequent
                 occurrence in layered elastic composite problems, and
                 this phenomenon is also captured by the boundary
                 integral equation system, demanding further
                 modification of the method of solution of the resulting
                 system of algebraic equations.",
  acknowledgement = ack-nhfb,
}

@TechReport{Stenger:2000:UAA,
  author =       "Frank Stenger",
  title =        "A unified approach to the approximate solution of
                 {PDE}",
  type =         "{Berichte aus der Technomathematik}",
  number =       "00-17",
  institution =  "{Zentrum f{\"u}r Technomathematik}",
  address =      "Bremen, Germany",
  pages =        "47",
  year =         "2000",
  bibdate =      "Wed May 09 10:34:27 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{Narasimhan:2002:FSA,
  author =       "S. Narasimhan and Kuan Chen and Frank Stenger",
  title =        "A first step in applying the {Sinc} collocation method
                 to the nonlinear {Navier--Stokes} equations",
  journal =      j-NUMER-HEAT-TRANSFER-B,
  volume =       "41",
  number =       "5",
  pages =        "447--462",
  year =         "2002",
  CODEN =        "NUHTD6",
  ISSN =         "1040-7790",
  ISSN-L =       "1040-7790",
  bibdate =      "Thu May 10 10:19:44 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Different numerical approaches have been proposed in
                 the past to solve the Navier--Stokes equations.
                 Conventional methods have often relied on
                 finite-difference, finite-element, and boundary-element
                 techniques. Multigrid methods have been recently
                 introduced because they help to obtain a faster
                 convergence rate of the error residual. A difficulty
                 plaguing numerical methods today is the inability to
                 treat singularities at or near boundaries. Such
                 difficulties become even more pronounced when coupled
                 with the need to handle semi-infinite and infinite
                 domains. Sinc-based numerical algorithms have the
                 advantage of handling singularities, boundary layers,
                 and semi-infinite domains very effectively. In
                 addition, they typically require fewer nodal points and
                 are proven to provide an exponential convergence rate
                 in solving linear differential equations. This study
                 involves a first step in applying the Sinc-based
                 algorithm to solve a nonlinear set of partial
                 differential equations. The example we consider arises
                 in the context of a driven-cavity flow in two space
                 dimensions. As such, the steady and incompressible
                 Navier--Stokes equations are solved by means of
                 two-dimensional Sinc collocation in conjunction with
                 the primitive variable method and a pressure correction
                 algorithm based on artificial compressibility.
                 Simulations are also carried out using forward
                 differences, central differences, and a commercial
                 code. Results are compared with one another and with
                 the Sinc-collocation approximation. It is found that
                 the error in the Sinc-collocation approximation
                 outperforms other solutions, especially near the
                 singular corners of the cavity.",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:2002:RFM,
  author =       "Frank Stenger and Elaine Cohen and Richard
                 Riesenfeld",
  title =        "Radial function methods of approximation based on
                 using harmonic {Green}'s functions",
  journal =      j-COMM-APPL-ANAL,
  volume =       "6",
  number =       "1",
  pages =        "1--15",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "1083-2564",
  MRclass =      "41A30 (41A63)",
  MRnumber =     "MR1879367 (2003e:41032)",
  MRreviewer =   "Valdir A. Menegatto",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In this paper we present an explicit method of radial
                 basis function approximation over $\Bbb R^n$, using the
                 Green's function for Laplace's equation. We prove
                 convergence of the scheme for all functions that are
                 continuous and of compact support. Interesting variants
                 of formulae result, in cases when lower dimensional
                 formulae are used to construct higher dimensional ones,
                 and in cases of periodic functions. Various explicit
                 operations are possible on the derived formulae, such
                 as obtaining Fourier and Hilbert transforms.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A30 (Approximation by other special function
                 classes) 41A63 (Multidimensional approximation
                 problems)",
  fjournal =     "Communications in Applied Analysis. An International
                 Journal for Theory and Applications",
  ZMnumber =     "1085.41509",
}

@InProceedings{Stenger:2002:SMA,
  author =       "Frank Stenger and Ahmad Reza Naghsh-Nilchi and Jenny
                 Niebsch and Ronny Ramlau",
  title =        "Sampling methods for approximate solution of {PDE}",
  crossref =     "Nashed:2002:IPI",
  pages =        "199--249",
  year =         "2002",
  MRclass =      "35A35 (44A35 65M70 65N35 65R20)",
  MRnumber =     "MR1940998 (2003m:35013)",
  MRreviewer =   "Stefka N. Dimova",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "The author proposed a novel procedure that combines
                 indefinite convolution and sine approximation, for
                 solving PDE. The PDE is first transformed to an
                 equivalent integral equation, this ``sine convolution''
                 procedure then enables solve the problem via method of
                 separation of variables. The method is flexible to
                 parallel computation. The time complexity of
                 computation to solve a $d$-dimensional problem on a
                 sequential machine is of the order
                 $(\log(\varepsilon))^{2d+2}$. Examples of solution are
                 illustrated for every type of equation.",
  acknowledgement = ack-nhfb,
  classmath =    "*35A35 (Theoretical approximation to solutions of PDE)
                 65M70 (Spectral, collocation and related methods (IVP
                 of PDE)) 65N35 (Collocation methods (BVP of PDE)) 65R20
                 (Integral equations (numerical methods))",
  keywords =     "Green's function; indefinite convolution; integral
                 equation; Laplace transformation; parallel computation;
                 separation of variables; sine approximation",
  reviewer =     "Qin Mengzhao (Beijing)",
  ZMnumber =     "1026.35006",
}

@TechReport{Stenger:2004:SCS,
  author =       "Frank Stenger",
  title =        "Sinc Convolution Solution of Laminated and Anisotropic
                 Composite Joints With Discrete Cracks",
  type =         "Technical Report",
  number =       "AD-b302 193",
  institution =  "Sinc. Inc.",
  address =      "Salt Lake City, UT, USA",
  pages =        "473",
  year =         "2004",
  bibdate =      "Wed May 09 10:38:58 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  acknowledgement = ack-nhfb,
}

@Article{Stenger:2004:SSB,
  author =       "Frank Stenger and Thomas Cook and Robert M. Kirby",
  title =        "{Sinc} solution of biharmonic problems",
  journal =      j-CAN-APPL-MATH-Q,
  volume =       "12",
  number =       "3",
  pages =        "391--414",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1073-1849",
  ISSN-L =       "1073-1849",
  MRclass =      "65N99",
  MRnumber =     "MR2178866 (2006h:65210)",
  MRreviewer =   "Nicolae Pop",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "We solve two biharmonic problems over a square,
                 $B=(-1, 1)\times(-1,1)$. (1) The problem $\nabla^4U=f$,
                 for which we determine a particular solution, $U$,
                 given $f$, via use of Sinc convolution; and (2) The
                 boundary value problem $\nabla^4V=0$ for which we
                 determine $V$ given $V=g$ and normal derivative $V_n=h$
                 on $\partial B$, the boundary of $B$. The solution to
                 this problem is carried out based on the identity
                 $$V=\Re\bigl\{\overline{(z-c)}{\cal E}+{\cal
                 F}\bigr\}=(x-a)u+ (y-b)v+\varphi,$$ where ${\cal
                 E}=u+iv$ and ${\cal F}=\varphi+ i\psi$ are functions
                 analytic in $B$, and where $c=a+ib$ is an arbitrary
                 constant. We thus determine approximations to the
                 harmonic functions $u,v$ and $\varphi$ on $\partial B$,
                 via use of Sinc quadrature, and Sinc approximation of
                 derivatives. We then use a special, explicit Sinc-based
                 analytic continuation procedure to extend the functions
                 $u,v$ and $\varphi$ to the interior of $B$. These
                 procedures enable us to determine functions $W$ which
                 solve a boundary problem at the form $\nabla^4W= f$ in
                 $B$, given $f$ in $B$ and given $W$ and its normal
                 derivative, $W_n$ on the boundary of $B$.\par

                 Given any $\varepsilon&gt;0$, the time complexity of
                 sequential computation of an approximation of
                 $W_\varepsilon$ to $W$ to within a uniform error of
                 $\varepsilon$ in $B$, i.e., such that $\sup_{(x,y)\in
                 B}|W(x,y)-W_\varepsilon (x,y)|&lt; \varepsilon$, is
                 $O((\log(\varepsilon))^6)$.",
  acknowledgement = ack-nhfb,
  classmath =    "*65N35 (Collocation methods (BVP of PDE)) 35J40
                 (Higher order elliptic equations, boundary value
                 problems) 65N15 (Error bounds (BVP of PDE)) 65N12
                 (Stability and convergence of numerical methods (BVP of
                 PDE))",
  fjournal =     "The Canadian Applied Mathematics Quarterly",
  keywords =     "biharmonic problems; collocation; convergence; error
                 bounds; numerical examples; Sinc convolution; Sinc
                 quadrature",
  ZMnumber =     "1096.65117",
}

@Article{Schmeisser:2007:SAG,
  author =       "Gerhard Schmeisser and Frank Stenger",
  title =        "Sinc approximation with a {Gaussian} multiplier",
  journal =      "Sampl. Theory Signal Image Process.",
  volume =       "6",
  number =       "2",
  pages =        "199--221",
  year =         "2007",
  bibdate =      "Tue Aug 24 23:09:55 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Recently, it was shown with the help of Fourier
                 analysis that by incorporating a Gaussian multiplier
                 into the truncated classical sampling series, one can
                 approximate bandlimited signals of finite energy with
                 an error that decays exponentially as a function of the
                 number of involved samples. Based on complex analysis,
                 we show for a slightly modified operator that this
                 approximation method applies not only to bandlimited
                 signals of finite energy, but also to bandlimited
                 signals of infinite energy, to classes of
                 non-bandlimited signals, to all entire functions of
                 exponential type (including those whose samples
                 increase exponentially), and to functions analytic in a
                 strip and not necessarily bounded. Moreover, the method
                 extends to non-real argument. In each of these cases,
                 the use of $2N+1$ samples results in an error bound of
                 the form $M{\text{e}}^{-\alpha N}$, where $M$ and
                 $\alpha$ are positive numbers that do not depend on
                 $N$. The power of the method is illustrated by several
                 examples.",
  acknowledgement = ack-nhfb,
  classmath =    "94A20 (Sampling theory); 30E10 (Approximation in the
                 complex domain); 65B10 (Summation of series (numerical
                 analysis))",
  keywords =     "error bounds, entire functions of exponential type;
                 functions analytic in a strip; Gaussian convergence
                 factor; sampling series; sinc approximation",
  language =     "English",
  ZMnumber =     "1156.94326",
}

@Article{Stenger:2007:SVS,
  author =       "Frank Stenger",
  title =        "Separation of variables solution of {PDE} via Sinc
                 methods",
  journal =      "Int. J. Appl. Math. Stat.",
  volume =       "10",
  number =       "SO7",
  pages =        "98--115",
  year =         "2007",
  bibdate =      "Tue Aug 24 23:09:55 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "In their 1953 text {\it P. M. Morse} and {\it H.
                 Feshbach} [Methods of theoretical physics. Vol. I. II.
                 (1953; Zbl 0051.40603)] list 13 regions of when the
                 three dimensional Laplace and Helmholtz partial
                 differential equation (PDE), can be solved via use of
                 separation of variables, i.e., via use of
                 one-dimensional methods. They describe explicit
                 transformations which make such solutions possible. In
                 this paper we state precise assumptions on the PDE, its
                 piecewise smooth curvilinear spatial boundary and the
                 boundary conditions, i.e., assumptions of analyticity
                 in each variable, which are satisfied, in essence,
                 whenever calculus is used to model the PDE. Under these
                 assumptions we are able to prove that the approximate
                 solution of the PDE has similar analyticity properties.
                 By combining this analyticity assumption with novel
                 sinc convolution methods, we are able to solve the PDE
                 to arbitrary uniform accuracy via use of a relatively
                 small sequence of one dimensional matrix
                 operations.

                 The proofs of the above claims are lengthy, and we
                 therefore present such proofs only for PDE in two
                 dimensions. Proofs for the case of three dimensional
                 will be published elsewhere.",
  acknowledgement = ack-nhfb,
  classmath =    "65N38 (Boundary element methods (BVP of PDE)) 35J05
                 (Laplacian operator, reduced wave equation (Helmholtz
                 equation), Poisson equation)",
  keywords =     "Dirichlet problem; Laplace equation; Neumann problem;
                 Poisson equation; separation of variables; sinc
                 convolution; sinc methods",
  language =     "English",
  ZMnumber =     "1139.65081",
}

@Article{Stenger:2008:FSZ,
  author =       "Frank Stenger",
  title =        "{Fourier} series for zeta function via {Sinc}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "429",
  number =       "10",
  pages =        "2636--2639",
  day =          "1",
  month =        nov,
  year =         "2008",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2008.01.037",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "11M06 (42A16)",
  MRnumber =     "2456801 (2009j:11135)",
  bibdate =      "Wed Aug 25 16:13:38 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.sciencedirect.com/science/journal/00243795",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
}

@Article{Stenger:2008:PAB,
  author =       "Frank Stenger and Brandon Baker and Carl Brewer and
                 Geoffrey Hunter and Sasha Kaputerko and Jason
                 Shepherd",
  title =        "Periodic approximations based on sinc",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "49",
  number =       "1",
  pages =        "63--72",
  year =         "2008",
  ISSN =         "1311-8080",
  ISSN-L =       "1314-3395",
  bibdate =      "Tue Aug 24 23:09:55 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "We derive some novel formulas for interpolating
                 functions that are periodic with period $T$ on $\Bbb
                 R=\{x: -\infty<x<\infty\}$. These formulas are all
                 based on the Whittaker Cardinal series expansion. We
                 give some comparative examples of approximations of
                 smooth periodic functions and discontinuous functions
                 via both our periodic basis as well as with
                 corresponding polynomial approximations.",
  acknowledgement = ack-nhfb,
  classmath =    "41A05 (Interpolation (approximations and
                 expansions))",
  keywords =     "cardinal expansions; Fourier polynomials;
                 interpolating functions, algebraic polynomials",
  language =     "English",
  ZMnumber =     "1169.41300",
}

@Article{Stenger:2009:PFD,
  author =       "Frank Stenger",
  title =        "Polynomial function and derivative approximation of
                 {Sinc} data",
  journal =      j-J-COMPLEXITY,
  volume =       "25",
  number =       "3",
  pages =        "292--302",
  year =         "2009",
  CODEN =        "JOCOEH",
  DOI =          "http://dx.doi.org/10.1016/j.jco.2009.02.010",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  bibdate =      "Tue Aug 24 23:09:55 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  abstract =     "Sinc methods consist of a family of one-dimensional
                 approximation procedures for approximating the
                 operations of calculus. These procedures are obtained
                 by operating on the sinc interpolation formulae, which
                 are based on the function values in the sinc points.
                 Usually, these operations yield high accuracy. However,
                 when differentiating a sinc approximation formula that
                 approximates over an interval with a finite endpoint,
                 then the accuracy is poor in the neighborhood of the
                 endpoint.\par

                 In the present paper the author derives a new way to
                 obtain an approximation of the derivative of a function
                 that is known in the sinc points. This method is proved
                 to be uniformly accurate over the whole interval. A
                 very simple example (the function $\sin(x)$ and its
                 derivative over the interval $[0,1]$) is studied
                 numerically to confirm the claimed accuracy.",
  acknowledgement = ack-nhfb,
  classmath =    "65D25 (Numerical differentiation) 65D10 (Smoothing,
                 curve fitting)",
  keywords =     "numerical differentiation; sinc interpolation; sinc
                 methods",
  reviewer =     "Willy Govaerts (Gent)",
  ZMnumber =     "1180.65028",
}

@Book{Stenger:2010:HSN,
  author =       "Frank Stenger",
  title =        "Handbook of Sinc Numerical Methods",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "xx + 463",
  year =         "2010",
  ISBN =         "1-4398-2158-5 (hardback), 1-4398-2159-3 (e-book)",
  ISBN-13 =      "978-1-4398-2158-9 (hardback), 978-1-4398-2159-6
                 (e-book)",
  LCCN =         "QA372 .S8195 2010",
  bibdate =      "Thu Mar 31 16:40:02 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Chapman and Hall/CRC numerical analysis and scientific
                 computation series",
  URL =          "http://www.crcpress.com/product/isbn/9781439821589",
  abstract =     "This handbook is essential for solving numerical
                 problems in mathematics, computer science, and
                 engineering. The methods presented are similar to
                 finite elements but more adept at solving analytic
                 problems with singularities over irregularly shaped yet
                 analytically described regions. The author makes sinc
                 methods accessible to potential users by limiting
                 details as to how or why these methods work. From
                 calculus to partial differential and integral
                 equations, the book can be used to approximate almost
                 every type of operation. It includes more than 470
                 MATLAB programs, along with a CD-ROM containing these
                 programs for ease of use",
  acknowledgement = ack-nhfb,
  subject =      "Galerkin methods; Differential equations; Numerical
                 solutions; mathematics / applied; mathematics /
                 differential equations; mathematics / number systems",
  tableofcontents = "One-Dimensional Sinc Theory \\
                 Introduction and Summary \\
                 Sampling over the Real Line \\
                 More General Sinc Approximation on $R$ \\
                 Sinc, Wavelets, Trigonometric and Algebraic Polynomials
                 and Quadratures \\
                 Sinc Methods on $\Gamma$ \\
                 Rational Approximation at Sinc Points \\
                 Polynomial Methods at Sinc Points \\
                 \\
                 Sinc Convolution-BIE Methods for PDE and IE \\
                 Introduction and Summary \\
                 Some Properties of Green's Functions \\
                 Free-Space Green's Functions for PDE \\
                 Laplace Transforms of Green's Functions \\
                 Multi-Dimensional Convolution Based on Sinc \\
                 Theory of Separation of Variables \\
                 \\
                 Explicit 1-d Program Solutions via Sinc-Pack \\
                 Introduction and Summary \\
                 Sinc Interpolation \\
                 Approximation of Derivatives \\
                 Sinc Quadrature \\
                 Sinc Indefinite Integration \\
                 Sinc Indefinite Convolution \\
                 Laplace Transform Inversion \\
                 Hilbert and Cauchy Transforms \\
                 Sinc Solution of ODE \\
                 Wavelet Examples \\
                 \\
                 Explicit Program Solutions of PDE via Sinc-Pack \\
                 Introduction and Summary \\
                 Elliptic PDE \\
                 Hyperbolic PDE \\
                 Parabolic PDE \\
                 Performance Comparisons \\
                 \\
                 Directory of Programs \\
                 Wavelet Formulas \\
                 One Dimensional Sinc Programs \\
                 Multi-Dimensional Laplace Transform Programs \\
                 \\
                 Bibliography \\
                 \\
                 Index",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Proceedings{Bettis:1974:POU,
  editor =       "Dale G. Bettis",
  booktitle =    "{Proceedings, 19--20 October 1972, the University of
                 Texas at Austin: Numerical solution of ordinary
                 differential equations}",
  title =        "{Proceedings, 19--20 October 1972, the University of
                 Texas at Austin: Numerical solution of ordinary
                 differential equations}",
  volume =       "362",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 490",
  year =         "1974",
  ISBN =         "0-387-06602-0 (New York)",
  ISBN-13 =      "978-0-387-06602-8 (New York)",
  LCCN =         "QA3 .L35; QA3 .L28 no. 362; QA372; QA3 .L28; QA1
                 .L471; QA3 .L4; QA372 .C765p 1972",
  bibdate =      "Wed May 9 08:44:50 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  meetingname =  "Conference on the Numerical Solution of Ordinary
                 Differential Equations (1972: University of Texas at
                 Austin)",
  remark =       "Sponsored jointly by the Society for Industrial and
                 Applied Mathematics and the Division of Dynamical
                 Astronomy of the American Astronomical Society.",
  subject =      "Differential equations; Numerical solutions;
                 Congresses; Many-body problem",
}

@Proceedings{Kirby:1974:OCT,
  editor =       "Bruce J. Kirby",
  booktitle =    "{Optimal control theory and its applications:
                 proceedings of the 14th biennial seminar of the
                 Canadian Mathematical Congress, University of Western
                 Ontario, Aug. 12--25, 1973}",
  title =        "{Optimal control theory and its applications:
                 proceedings of the 14th biennial seminar of the
                 Canadian Mathematical Congress, University of Western
                 Ontario, Aug. 12--25, 1973}",
  volume =       "106",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "403",
  year =         "1974",
  ISBN =         "3-540-07026-5",
  ISBN-13 =      "978-3-540-07026-9",
  ISSN =         "0075-8442",
  LCCN =         "QA402.3 C33 1974",
  bibdate =      "Wed May 9 10:30:57 MDT 2007",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 sirsi.library.utoronto.ca:2200/UNICORN",
  series =       "Lecture notes in economics and mathematical systems",
  acknowledgement = ack-nhfb,
}

@Proceedings{Allgower:1981:NSN,
  editor =       "E. L. (Eugene L.) Allgower and Klaus Glashoff and
                 Heinz-Otto Peitgen",
  booktitle =    "{Numerical solution of nonlinear equations:
                 proceedings, Bremen, 1980}",
  title =        "{Numerical solution of nonlinear equations:
                 proceedings, Bremen, 1980}",
  volume =       "878",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 440",
  year =         "1981",
  ISBN =         "0-387-10871-8",
  ISBN-13 =      "978-0-387-10871-1",
  LCCN =         "QA3 .L471 no.878; QA3.L471",
  bibdate =      "Wed May 9 09:06:42 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 library.mit.edu:9909/mit01",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Symposium held July 21-25, 1980, under the sponsorship
                 of the Forschungsschwerpunkt ``Dynamische Systeme'',
                 Universit{\"a}t Bremen, and the W. Blaschke
                 Gesellschaft, Hamburg.",
  subject =      "Differential equations, Nonlinear; Numerical
                 solutions; Congresses",
}

@Proceedings{McAvoy:1983:IUS,
  editor =       "B. R. McAvoy",
  booktitle =    "{IEEE 1983 Ultrasonics Symposium: October 31, November
                 1-2, 1983, Atlanta Marriott Hotel, Atlanta, Georgia}",
  title =        "{IEEE 1983 Ultrasonics Symposium: October 31, November
                 1-2, 1983, Atlanta Marriott Hotel, Atlanta, Georgia}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1180",
  year =         "1983",
  CODEN =        "ULSPDT",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0090-5607",
  LCCN =         "????",
  bibdate =      "Wed May 09 18:26:26 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Two volumes. IEEE catalog number 83CH1947-1.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Graves-Morris:1984:RAI,
  editor =       "P. R. Graves-Morris and E. B. Saff and Richard S.
                 Varga",
  booktitle =    "{Rational approximation and interpolation: proceedings
                 of the United Kingdom--United States conference held at
                 Tampa, Florida, December 12--16, 1983}",
  title =        "{Rational approximation and interpolation: proceedings
                 of the United Kingdom--United States conference held at
                 Tampa, Florida, December 12--16, 1983}",
  volume =       "1105",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 528",
  year =         "1984",
  ISBN =         "0-387-13899-4",
  ISBN-13 =      "978-0-387-13899-2",
  LCCN =         "QA3 .L471 no.1105; QA3.L471",
  bibdate =      "Wed May 9 09:11:28 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 library.mit.edu:9909/mit01",
  price =        "DM72.00",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Conference on Rational Approximation and
                 Interpolation, held 12/12--16/83 in Tampa, Fla., and
                 sponsored by the US National Science Foundation and the
                 UK Science and Engineering Research Council.",
  subject =      "Approximation theory; Congresses; Interpolation",
}

@Proceedings{Kaveh:1984:AI,
  editor =       "M. Kaveh and R. K. Mueller and J. F. Greenleaf",
  booktitle =    "{Acoustical imaging: Proceedings of the thirteenth
                 International Symposium on Acoustical Imaging, held
                 October 26--28, 1983, in Minneapolis, MN}",
  title =        "{Acoustical imaging: Proceedings of the thirteenth
                 International Symposium on Acoustical Imaging, held
                 October 26--28, 1983, in Minneapolis, MN}",
  volume =       "13",
  publisher =    pub-PLENUM,
  address =      pub-PLENUM:adr,
  pages =        "xii + 605",
  year =         "1984",
  CODEN =        "ACIGD9",
  ISBN =         "0-306-41717-0",
  ISBN-13 =      "978-0-306-41717-7",
  ISSN =         "0270-5117",
  LCCN =         "????",
  bibdate =      "Wed May 9 19:29:39 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Acoustical imaging",
  acknowledgement = ack-nhfb,
}

@Proceedings{Miller:1984:CMA,
  editor =       "Anthony Miller",
  booktitle =    "{Contributions of mathematical analysis to the
                 numerical solution of partial differential equations}",
  title =        "{Contributions of mathematical analysis to the
                 numerical solution of partial differential equations}",
  volume =       "7",
  publisher =    "Centre for Mathematical Analysis, Australian National
                 University",
  address =      "Canberra, Australia",
  pages =        "v + 213",
  year =         "1984",
  ISBN =         "0-86784-508-2",
  ISBN-13 =      "978-0-86784-508-2",
  LCCN =         "QA374 .C661 1984",
  bibdate =      "Wed May 9 08:52:55 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Proceedings of the Centre for Mathematical Analysis,
                 Australian National University",
  acknowledgement = ack-nhfb,
  subject =      "Differential equations, Partial; Numerical solutions;
                 Congresses",
}

@Proceedings{McAvoy:1985:IUS,
  editor =       "B. R. McAvoy",
  booktitle =    "{IEEE 1985 Ultrasonics Symposium: October 16--18,
                 1985, Cathedral Hill Hotel, San Francisco,
                 California}",
  title =        "{IEEE 1985 Ultrasonics Symposium: October 16--18,
                 1985, Cathedral Hill Hotel, San Francisco,
                 California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1146",
  year =         "1985",
  CODEN =        "ULSPDT",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0090-5607",
  LCCN =         "TA367 U47 1985 v. 1-2",
  bibdate =      "Wed May 09 18:26:26 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Two volumes. IEEE catalog number 85CH2209-5.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Nalcioglu:1986:IWP,
  editor =       "O. (Orhan) Nalcioglu and Z.-H. (Zang-Hee) Cho and
                 Thomas F. (Thomas Francis) Budinger and others",
  booktitle =    "{International Workshop on Physics and Engineering of
                 Computerized Multidimensional Imaging and Processing:
                 2--4 April 1986, Newport Beach, California}",
  title =        "{International Workshop on Physics and Engineering of
                 Computerized Multidimensional Imaging and Processing:
                 2--4 April 1986, Newport Beach, California}",
  volume =       "671",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "viii + 329",
  year =         "1986",
  CODEN =        "PSISDG",
  ISBN =         "0-89252-706-4",
  ISBN-13 =      "978-0-89252-706-9",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  LCCN =         "TK8315 .I5451 1986; TK8315 .I57 1986; TA1632 .I62
                 1986; TS510 .S63; TA1632 .I58 1986",
  bibdate =      "Wed May 9 19:25:40 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "SPIE",
  acknowledgement = ack-nhfb,
  meetingname =  "International Workshop on Physics and Engineering of
                 Computerized Multidimensional Imaging and Processing
                 (1986: Newport Beach, Calif.)",
  subject =      "Image processing; Digital techniques; Congresses;
                 Imaging systems",
}

@Proceedings{Jones:1987:AIP,
  editor =       "Hugh W. Jones",
  booktitle =    "{Acoustical Imaging: Proceedings of the International
                 Symposium, July 14--16, 1986, Halifax, NS, Canada}",
  title =        "{Acoustical Imaging: Proceedings of the International
                 Symposium, July 14--16, 1986, Halifax, NS, Canada}",
  volume =       "15",
  publisher =    pub-PLENUM,
  address =      pub-PLENUM:adr,
  pages =        "xi + 692",
  year =         "1987",
  CODEN =        "ACIGD9",
  ISBN =         "0-306-42565-3",
  ISBN-13 =      "978-0-306-42565-3",
  ISSN =         "0270-5117",
  LCCN =         "????",
  bibdate =      "Wed May 9 19:29:45 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Acoustical imaging",
  acknowledgement = ack-nhfb,
  remark =       "Proceedings of the 15th International Symposium on
                 Acoustical Imaging, held in Halifax, Nova Scotia,
                 Canada'' - Tittelsidens bakside.",
}

@Proceedings{Bowers:1989:CCP,
  editor =       "K. Bowers and J. Lund and K. L. (Kenneth L.) Bowers
                 and J. (John) Lund",
  booktitle =    "{Computation and control: proceedings of the Bozeman
                 conference, Bozeman, Montana, August 1--11, 1988}",
  title =        "{Computation and control: proceedings of the Bozeman
                 conference, Bozeman, Montana, August 1--11, 1988}",
  volume =       "1",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "410",
  year =         "1989",
  ISBN =         "0-8176-3438-X",
  ISBN-13 =      "978-0-8176-3438-4",
  LCCN =         "TA329 .C645 1989",
  bibdate =      "Wed May 9 08:56:08 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Progress in systems and control theory",
  acknowledgement = ack-nhfb,
  remark =       "``Collection of papers \ldots{} delivered at the first
                 Bozeman Conference on Computation and Control, held at
                 Montana State University''--Pref.",
  subject =      "Engineering mathematics; Congresses; Feedback control
                 systems",
}

@Proceedings{Martin:1990:VSL,
  editor =       "Clyde Martin and John White",
  booktitle =    "{Visiting scholars' lectures 1989, Texas Tech
                 University, Lubbock, TX (USA)}",
  title =        "{Visiting scholars' lectures 1989, Texas Tech
                 University, Lubbock, TX (USA)}",
  volume =       "16",
  publisher =    "Department of Mathematics, Texas Tech University",
  address =      "Lubbock, TX, USA",
  pages =        "113",
  year =         "1990",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  series =       "Mathematics Series",
  acknowledgement = ack-nhfb,
  classmath =    "*00Bxx (Conference proceedings and collections of
                 papers)",
  keywords =     "Lectures; Lubbock, TX (USA); Texas Tech University;
                 Visiting scholars' lectures",
  ZMnumber =     "0695.00001",
}

@Proceedings{Wong:1990:ACA,
  editor =       "R. (Roderick) Wong",
  booktitle =    "{Asymptotic and computational analysis: conference in
                 honor of Frank W. J. Olver's 65th birthday}",
  title =        "{Asymptotic and computational analysis: conference in
                 honor of Frank W. J. Olver's 65th birthday}",
  volume =       "124",
  publisher =    pub-MARCEL-DEKKER,
  address =      pub-MARCEL-DEKKER:adr,
  pages =        "xii + 755",
  year =         "1990",
  ISBN =         "0-8247-8347-6",
  ISBN-13 =      "978-0-8247-8347-1",
  LCCN =         "QA299.6 .A88 1990",
  bibdate =      "Wed May 9 09:22:13 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in pure and applied mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0647/90002810-d.html",
  abstract =     "Papers presented at the International Symposium on
                 Asymptotic and Computational Analysis, held June 1989,
                 Winnipeg, Man., sponsored by the Dept. of Applied
                 Mathematics, University of Manitoba and the Canadian
                 Applied Mathematics Society.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Congresses; Asymptotic expansions;
                 Olver, Frank W. J.",
  subject-dates = "1924--",
}

@Proceedings{Bowers:1991:CCI,
  editor =       "K. L. (Kenneth L.) Bowers and J. (John) Lund",
  booktitle =    "{Computation and control II: proceedings of the second
                 Bozeman conference, Bozeman, Montana, August 1--7,
                 1990}",
  title =        "{Computation and control II: proceedings of the second
                 Bozeman conference, Bozeman, Montana, August 1--7,
                 1990}",
  volume =       "11",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "369",
  year =         "1991",
  ISBN =         "0-8176-3611-0",
  ISBN-13 =      "978-0-8176-3611-1",
  LCCN =         "TA329 .C644 1991",
  bibdate =      "Wed May 9 08:56:08 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$65.00",
  series =       "Progress in systems and control theory",
  acknowledgement = ack-nhfb,
  subject =      "Engineering mathematics; Congresses; Feedback control
                 systems",
}

@Proceedings{Genz:1992:NIR,
  editor =       "Alan Genz and Terje O. Espelid",
  booktitle =    "{Numerical integration: recent developments, software
                 and applications}",
  title =        "{Numerical integration: recent developments, software
                 and applications}",
  volume =       "357",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xii + 367",
  year =         "1992",
  ISBN =         "0-7923-1583-9",
  ISBN-13 =      "978-0-7923-1583-4",
  LCCN =         "QA299.3 .N38 1991",
  bibdate =      "Wed May 9 09:35:28 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "NATO ASI series. Series C, Mathematical and physical
                 sciences",
  acknowledgement = ack-nhfb,
  meetingname =  "NATO Advanced Research Workshop on Numerical
                 Integration: Recent Developments, Software and
                 Applications. Bergen. 1991",
  remark =       "Proceedings of the NATO Advanced Research Workshop on
                 Numerical Integration: Recent Developments, Software
                 and Applications, Bergen, Norway, June 17--21, 1991.",
  subject =      "Numerical integration; Congresses;
                 Differensialligninger; Databehandling; Numerisk
                 l{\o}sning",
}

@Proceedings{Zahar:1994:ACF,
  editor =       "R. V. M. (Ramsay Vincent Michael) Zahar",
  booktitle =    "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  title =        "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  volume =       "119",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xlvi + 591",
  year =         "1994",
  ISBN =         "0-8176-3753-2",
  ISBN-13 =      "978-0-8176-3753-8",
  LCCN =         "QA221 .A634 1994",
  bibdate =      "Wed May 9 09:01:57 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series of numerical mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Approximation theory; Congresses; Orthogonal
                 polynomials; Numerical integration; Functions,
                 Special",
}

@Proceedings{Ang:1995:IPA,
  editor =       "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and
                 others",
  title =        "{Inverse problems and applications to geophysics,
                 industry, medicine and technology: proceedings of the
                 International Workshop on Inverse Problems, 17--19
                 January 1995, Ho Chi Minh City}",
  volume =       "2",
  publisher =    "Vietnam Mathematical Society",
  address =      "Ho Chi Minh City, Vietnam",
  pages =        "226",
  year =         "1995",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed May 09 17:36:40 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  series =       "Publications of the Ho Chi Minh City Mathematical
                 Society",
  acknowledgement = ack-nhfb,
}

@Proceedings{Ismail:1995:MAW,
  editor =       "Mourad Ismail and others",
  booktitle =    "{Mathematical analysis, wavelets, and signal
                 processing: an International Conference on Mathematical
                 Analysis and Signal Processing, January 3--9, 1994,
                 Cairo University, Cairo, Egypt}",
  title =        "{Mathematical analysis, wavelets, and signal
                 processing: an International Conference on Mathematical
                 Analysis and Signal Processing, January 3--9, 1994,
                 Cairo University, Cairo, Egypt}",
  volume =       "190",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 354",
  year =         "1995",
  ISBN =         "0-8218-0384-0",
  ISBN-13 =      "978-0-8218-0384-4",
  ISSN =         "0271-4132 (print), 1098-3627 (electronic)",
  LCCN =         "QA299.6 .M38 1995",
  bibdate =      "Wed May 9 08:38:41 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Contemporary mathematics",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Mathematical Analysis and
                 Signal Processing (1994: Cairo, Egypt)",
  subject =      "Mathematical analysis; Congresses; Wavelets
                 (Mathematics); Signal processing; Mathematics",
}

@Proceedings{Papamichael:1999:CMF,
  editor =       "N. (Nicolas) Papamichael and Stephan Ruscheweyh and E.
                 B. Saff",
  booktitle =    "{Computational methods and function theory 1997:
                 proceedings of the Third CMFT Conference, 13--17
                 October 1997, Nicosia, Cyprus}",
  title =        "{Computational methods and function theory 1997:
                 proceedings of the Third CMFT Conference, 13--17
                 October 1997, Nicosia, Cyprus}",
  volume =       "11",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xi + 652",
  year =         "1999",
  ISBN =         "981-02-3626-3",
  ISBN-13 =      "978-981-02-3626-7",
  LCCN =         "QA297 .I473 1997",
  bibdate =      "Wed May 9 09:40:29 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Series in approximations and decompositions",
  acknowledgement = ack-nhfb,
  meetingname =  "CMFT Conference (3rd: 1997: Nicosia, Cyprus)",
  subject =      "Numerical analysis; Congresses; Functions of complex
                 variables",
}

@Proceedings{Kromann:2000:ISI,
  editor =       "Gary B. Kromann and J. Richard Culham and Koneru
                 Ramakrishna",
  booktitle =    "{ITherm 2000: the Seventh Intersociety Conference on
                 Thermal and Thermomechanical Phenomena in Electronic
                 Systems, presented at Las Vegas, Nevada, USA, May
                 23--26, 2000}",
  title =        "{ITherm 2000: the Seventh Intersociety Conference on
                 Thermal and Thermomechanical Phenomena in Electronic
                 Systems, presented at Las Vegas, Nevada, USA, May
                 23--26, 2000}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + viii + 819",
  year =         "2000",
  ISBN =         "0-7803-5912-7 (softcover), 0-7803-5913-5 (casebound),
                 0-7803-5914-3 (microfiche)",
  ISBN-13 =      "978-0-7803-5912-3 (softcover), 978-0-7803-5913-0
                 (casebound), 978-0-7803-5914-7 (microfiche)",
  LCCN =         "TK7870.25 .I6 2000",
  bibdate =      "Wed May 09 18:22:15 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
  note =         "Two volumes. IEEE catalog number 00CH37069.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Nashed:2002:IPI,
  editor =       "M. Zuhair Nashed and Otmar Scherzer",
  booktitle =    "{Inverse problems, image analysis, and medical
                 imaging: AMS Special Session on Interaction of Inverse
                 Problems and Image Analysis, January 10--13, 2001, New
                 Orleans, Louisiana}",
  title =        "{Inverse problems, image analysis, and medical
                 imaging: AMS Special Session on Interaction of Inverse
                 Problems and Image Analysis, January 10--13, 2001, New
                 Orleans, Louisiana}",
  volume =       "313",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 305",
  year =         "2002",
  ISBN =         "0-8218-2979-3",
  ISBN-13 =      "978-0-8218-2979-0",
  LCCN =         "TA1637 .A47 2001",
  bibdate =      "Wed May 9 09:41:07 MDT 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Contemporary mathematics, 0271-4132",
  acknowledgement = ack-nhfb,
  meetingname =  "AMS Special Session on Interaction of Inverse Problems
                 and Image Analysis (2001: New Orleans, LA)",
  subject =      "Image processing; Digital techniques; Mathematical
                 models; Congresses; Image analysis; Inverse problems
                 (Differential equations); Diagnostic imaging;
                 Mathematic models",
}